تكلم مع الذكاء الاصطناعي
Deck 8: Further Applications of Integration
ملء الشاشة (f)
سؤال
A demand curve is given by 
.
Find the consumer surplus when the selling price is $
.
.Find the consumer surplus when the selling price is $
.
سؤال
The marginal revenue from producing x units of a certain product is 
(in dollars per unit). Find the increase in revenue if the production level is raised from 1,100 units to 
units.
A)$
B)$51367000
C)$26866667
D)$17765250
E)$37974583
(in dollars per unit). Find the increase in revenue if the production level is raised from 1,100 units to units.A)$
B)$51367000
C)$26866667
D)$17765250
E)$37974583
سؤال
For any normal distribution, find 
to two decimal places.
to two decimal places. سؤال
You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.) 
A)208 lb
B)104 lb
C)1040 lb
D)520 lb
A)208 lb
B)104 lb
C)1040 lb
D)520 lb
سؤال
The manager of a fast-food restaurant determines that the average time that her customers wait for service is 2 minutes. Find the probability that a customer is served within the first 
minutes.
A)
B)
C)
D)
E)
minutes.A)
B)
C)
D)
E)
سؤال
For a given commodity and pure competition, the number of units produced and the price per unit are determined as the coordinates of the point of intersection of the supply and demand curves. Given the demand curve 
and the supply curve 
,
find the consumer surplus.
and the supply curve ,find the consumer surplus.
سؤال
A hot, wet summer is causing a mosquito population explosion in a lake resort area. The number of mosquitoes is increasing at an estimated rate of 
per week (where t is measured in weeks). By how much does the mosquito population increase between the 4th and 
th weeks of summer?
A)5702
B)6702
C)8702
D)7702
E)
per week (where t is measured in weeks). By how much does the mosquito population increase between the 4th and th weeks of summer?A)5702
B)6702
C)8702
D)7702
E)
سؤال
A movie theater has been charging $ 
.00 per person and selling about 
tickets on a typical weeknight. After surveying their customers, the theater estimates that for every $ 
that they lower the price, the number of moviegoers will increase by 
per night. Find the demand function and calculate the consumer surplus when the tickets are priced at $ 
.
.00 per person and selling about tickets on a typical weeknight. After surveying their customers, the theater estimates that for every $ that they lower the price, the number of moviegoers will increase by per night. Find the demand function and calculate the consumer surplus when the tickets are priced at $ . سؤال
The manager of a fast-food restaurant determines that the average time that her customers wait for service is 2 minutes.
The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than
% of her customers. What value of x must she use in the advertisement "if you aren't served within x minutes, you get a free hamburger"?
The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than
% of her customers. What value of x must she use in the advertisement "if you aren't served within x minutes, you get a free hamburger"? سؤال
Boxes are labeled as containing 500 g of cereal. The machine filling the boxes produces weights that are normally distributed with standard deviation 12
g.If the target weight is 500 g, what is the probability that the machine produces a box with less than
g of cereal? Round your answer to four decimal places.
g.If the target weight is 500 g, what is the probability that the machine produces a box with less than
g of cereal? Round your answer to four decimal places. سؤال
Let 
a) For what value of c is f a probability density function?
b) For that value of c, find P (-1 < X < 1).
a) For what value of c is f a probability density function?
b) For that value of c, find P (-1 < X < 1).
سؤال
If f (x) is the probability density function for the blood cholesterol level of men over the age of 40, where x is measured in milligrams per deciliter, express as an integral the probability that the cholesterol level of such a man lies between 195 and 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Suppose the average waiting time for a customer's call to be answered by a company representative (modeled by exponentially decreasing probability density functions) is 
minutes. Find the median waiting time.
A)
minutes
B)
minutes
C)
minutes
D)
minutes
E)
minutes
minutes. Find the median waiting time.A)
minutesB)
minutesC)
minutesD)
minutesE)
minutes سؤال
You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.) 
A)332.8 lb
B)1331.2 lb
C)2662.4 lb
D)665.6 lb
A)332.8 lb
B)1331.2 lb
C)2662.4 lb
D)665.6 lb
سؤال
The demand function for a commodity is given by 
. Find the consumer surplus when the sales level is 
.
A)$9458
B)$10458
C)$
D)$8458
E)$4458
. Find the consumer surplus when the sales level is .A)$9458
B)$10458
C)$
D)$8458
E)$4458
سؤال
A type of lightbulb is labeled as having an average lifetime of 
hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean µ = 
. What is the median lifetime of these lightbulbs? Give your answer rounded to two decimal places.
hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean µ = . What is the median lifetime of these lightbulbs? Give your answer rounded to two decimal places. سؤال
Let the function whose graph is shown be a probability density function. Calculate the mean. 
سؤال
The standard deviation for a random variable with probability density function f and mean µ is defined 
. Find the standard deviation for an exponential density function with mean 
.
A)
B)
C)
D)
E)
. Find the standard deviation for an exponential density function with mean .A)
B)
C)
D)
E)
سؤال
The marginal cost function 
is defined to be the derivative of the cost function. If the marginal cost of manufacturing x units of a product is 
(measured in dollars per unit) and the fixed start-up cost is 
, use the Total Change Theorem to find the cost of producing the first 5,000 units.
A)$35,444,500
B)$
C)$35,434,500
D)$35,454,500
E)$35,484,500
is defined to be the derivative of the cost function. If the marginal cost of manufacturing x units of a product is (measured in dollars per unit) and the fixed start-up cost is , use the Total Change Theorem to find the cost of producing the first 5,000 units.A)$35,444,500
B)$
C)$35,434,500
D)$35,454,500
E)$35,484,500
سؤال
A gate in an irrigation canal is constructed in the form of a trapezoid 
ft wide at the bottom, 
ft wide at the top, and 2 ft high. It is placed vertically in the canal, with the water extending to its top. Find the hydrostatic force on one side of the gate..
A)
lb
B)
lb
C)
lb
D)
lb
E)None of these
ft wide at the bottom, ft wide at the top, and 2 ft high. It is placed vertically in the canal, with the water extending to its top. Find the hydrostatic force on one side of the gate..A)
lbB)
lbC)
lbD)
lbE)None of these
سؤال
The masses 
are located at the point 
. Find the moments 
and 
and the center of mass of the system. 
; 
A)
B)
C)
D)
E)
are located at the point . Find the moments and and the center of mass of the system. ; A)
B)
C)
D)
E)
سؤال
سؤال
A swimming pool is 10 ft wide and 36 ft long and its bottom is an inclined plane, the shallow end having a depth of 
ft and the deep end, 12 ft. If the pool is full of water, find the hydrostatic force on the shallow end. (Use the fact that water weighs 62.5 lb/ 
.)
ft and the deep end, 12 ft. If the pool is full of water, find the hydrostatic force on the shallow end. (Use the fact that water weighs 62.5 lb/ .) سؤال
Find the center of mass of a lamina in the shape of a quarter-circle with radius 
with density 
= 
. 
with density = . سؤال
Find the centroid of the region shown, not by integration, but by locating the centroids of the
rectangles and triangles and using additivity of moments.
rectangles and triangles and using additivity of moments.
سؤال
Find the centroid of the region bounded by the graphs of the given equations. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Calculate the center of mass of the lamina with density 
= 
. 
= . سؤال
Find the exact coordinates of the centroid. 
سؤال
سؤال
A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find the force exerted by the water on the plate. (The weight density of water is 62.4 lb/ft3.) 
(ft)
A)124.8 lb
B)436.8 lb
C)873.6 lb
D)62.4 lb
(ft)A)124.8 lb
B)436.8 lb
C)873.6 lb
D)62.4 lb
سؤال
Find the coordinates of the centroid for the region bounded by the curves 
, x = 0,
and y =
.
, x = 0,and y =
. سؤال
Use the Theorem of Pappus to find the volume of the solid obtained by revolving the region bounded by the graphs of 
and 
about the y-axis.
A) 144
B) 108
C) 648
D) 864
and about the y-axis.A) 144
B) 108
C) 648
D) 864
سؤال
Find the centroid of the region bounded by the curves. 
سؤال
Find the centroid of the region bounded by the given curves. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the centroid of the region bounded by the given curves. 
سؤال
You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.) 
سؤال
A trough is filled with a liquid of density 855 kg/ 
. The ends of the trough are equilateral triangles with sides 
m long and vertex at the bottom. Find the hydrostatic force on one end of the trough.
A)
B)
C)
D)
E)
. The ends of the trough are equilateral triangles with sides m long and vertex at the bottom. Find the hydrostatic force on one end of the trough.A)
B)
C)
D)
E)
سؤال
سؤال
Find the centroid of the region bounded by the given curves. 
A)
B)
C)
D)
E)None of these
A)
B)
C)
D)
E)None of these
سؤال
Find the centroid of the region bounded by the graphs of the given equations. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
سؤال
سؤال
Find the volume obtained when the circle of radius 
with center ( 
, 0) is rotated about the y-axis.
A)
B)
C)
D)
E)
with center ( , 0) is rotated about the y-axis.A)
B)
C)
D)
E)
سؤال
Find the centroid of the region bounded by the graphs of 
and 
.
and . سؤال
Find the centroid of the region shown in the figure. 
سؤال
A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find the force exerted by the water on the plate. (The weight density of water is 62.4 lb/ft3.) 
(ft)
(ft) سؤال
Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve 
about the x-axis on the interval 
.
A)
B)
C)
D)
E)
about the x-axis on the interval .A)
B)
C)
D)
E)
سؤال
You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.) 
سؤال
Write an integral giving the area of the surface obtained by revolving the curve about the x-axis. (Do not evaluate the integral.) y = ![<strong>Write an integral giving the area of the surface obtained by revolving the curve about the x-axis. (Do not evaluate the integral.) y = on [3, 6]</strong> A)2 \pi B)2 \pi C)8 \pi D)8 \pi <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_553a_3e8f_9f8f_a97e0dddc6ee_TB5971_11.jpg)
on [3, 6]
A)2![<strong>Write an integral giving the area of the surface obtained by revolving the curve about the x-axis. (Do not evaluate the integral.) y = on [3, 6]</strong> A)2 \pi B)2 \pi C)8 \pi D)8 \pi <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_553a_3e90_9f8f_4740ec3f571f_TB5971_11.jpg)
B)2![<strong>Write an integral giving the area of the surface obtained by revolving the curve about the x-axis. (Do not evaluate the integral.) y = on [3, 6]</strong> A)2 \pi B)2 \pi C)8 \pi D)8 \pi <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_553a_3e91_9f8f_e35d80265f45_TB5971_11.jpg)
C)8![<strong>Write an integral giving the area of the surface obtained by revolving the curve about the x-axis. (Do not evaluate the integral.) y = on [3, 6]</strong> A)2 \pi B)2 \pi C)8 \pi D)8 \pi <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_553a_65a2_9f8f_99273e5c97f3_TB5971_11.jpg)
D)8![<strong>Write an integral giving the area of the surface obtained by revolving the curve about the x-axis. (Do not evaluate the integral.) y = on [3, 6]</strong> A)2 \pi B)2 \pi C)8 \pi D)8 \pi <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_553a_65a3_9f8f_d981be9e648a_TB5971_11.jpg)
on [3, 6]A)2
B)2
C)8
D)8
سؤال
Find the area of the surface obtained by rotating the curve about the x-axis. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the center of mass of the lamina of the region shown if the density of the circular lamina is five times that of the rectangular lamina. 
سؤال
You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.) 
سؤال
A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find the force exerted by the water on the plate. (The weight density of water is 62.4 lb/ft3.) 
(ft)
(ft) سؤال
Find the area of the surface obtained by rotating the curve about the y-axis. 
A)
B)
C)
D)
E)None of these
A)
B)
C)
D)
E)None of these
سؤال
Find the area of the surface obtained by revolving the given curve about the x-axis. 
on 
A)
B)
C)
D)
on A)
B)
C)
D)
سؤال
Find the centroid of the region bounded by the graphs of 
and 
.
and . سؤال
Find the area of the surface obtained by rotating the circle 
about the line 
.
A)
B)
C)
D)
E)
about the line .A)
B)
C)
D)
E)
سؤال
Find the area of the region under the graph of f on [a, b]. ![<strong>Find the area of the region under the graph of f on [a, b]. </strong> A)6 B)-3 C)3 D)-6 <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_5539_a248_9f8f_7769319804f5_TB5971_11.jpg)
A)6
B)-3
C)3
D)-6
A)6
B)-3
C)3
D)-6
سؤال
Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about the given axis. 
y-axis
A)
B)
C)
D)
E)
y-axisA)
B)
C)
D)
E)
سؤال
Find the centroid of the region bounded by the graphs of the given equations. 
سؤال
Use differentials to approximate the arc length of the graph of the equation from P to Q. Round answer to four decimal places. 
P (3, 12), Q (3.2, 13.24)
A)2.4331
B)1.2166
C)3.6497
D)6.0828
P (3, 12), Q (3.2, 13.24)A)2.4331
B)1.2166
C)3.6497
D)6.0828
سؤال
Find the arc length function for the curve 
with starting point 
.
A)
B)
C)
D)
E)
with starting point .A)
B)
C)
D)
E)
سؤال
Find the arc length of the graph from A to B. 
A)
)
B)
)
C)
)
D)
)
A)
)B)
)C)
)D)
) سؤال
If the infinite curve 
, is rotated about the x-axis , find the area of the resulting surface.
A)
B)
C)
D)
E)
, is rotated about the x-axis , find the area of the resulting surface.A)
B)
C)
D)
E)
سؤال
Find the length of the curve. 
A)
B)
C)
D)
E)None of these
A)
B)
C)
D)
E)None of these
سؤال
Find the area of the surface obtained by revolving the given curve about the y-axis.
x =![Find the area of the surface obtained by revolving the given curve about the y-axis. x = on [0, 2]<div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_553a_dadd_9f8f_81d3846dad61_TB5971_11.jpg)
on [0, 2]
x =
on [0, 2] سؤال
Find the length of the curve. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the area of the surface obtained by revolving the graph of y = ![Find the area of the surface obtained by revolving the graph of y = on [0, 1] about the x-axis.<div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_553a_dade_9f8f_6b02730e1e36_TB5971_11.jpg)
on [0, 1] about the x-axis.
on [0, 1] about the x-axis. سؤال
Set up, but do not evaluate, an integral for the length of the curve. 
سؤال
Set up, but do not evaluate, an integral that represents the length of the curve. 
سؤال
Use Simpson's Rule with n = 6 to estimate the length of the curve 
, 
. Round your answer to six decimal places.
A)6.987208
B)6.972089
C)6.947582
D)6.947368
E)None of these
, . Round your answer to six decimal places.A)6.987208
B)6.972089
C)6.947582
D)6.947368
E)None of these
سؤال
Find the area of the surface obtained by revolving the given curve about the x-axis. ![Find the area of the surface obtained by revolving the given curve about the x-axis. on [0, 1]<div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_553b_01ef_9f8f_6feec30a6ad6_TB5971_11.jpg)
on [0, 1]
on [0, 1] سؤال
Find the length of the curve. 
A)36.05
B)13.05
C)
D)25.05
E)None of these
A)36.05
B)13.05
C)
D)25.05
E)None of these
سؤال
Find the area of the surface obtained by rotating the curve about the 
-axis. 
-axis. سؤال
Find the arc length of the graph of the given equation on the specified interval. y = ![<strong>Find the arc length of the graph of the given equation on the specified interval. y = ( + 1) <sup> </sup> , [2, 5]</strong> A) B) C) D) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_553c_1380_9f8f_450ae464b98e_TB5971_11.jpg)
( ![<strong>Find the arc length of the graph of the given equation on the specified interval. y = ( + 1) <sup> </sup> , [2, 5]</strong> A) B) C) D) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_553c_1381_9f8f_9deb21f7ecd2_TB5971_11.jpg)
+ 1) ![<strong>Find the arc length of the graph of the given equation on the specified interval. y = ( + 1) <sup> </sup> , [2, 5]</strong> A) B) C) D) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_553c_1382_9f8f_9f437e425dc8_TB5971_11.jpg)
, [2, 5]
A)![<strong>Find the arc length of the graph of the given equation on the specified interval. y = ( + 1) <sup> </sup> , [2, 5]</strong> A) B) C) D) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_553c_3a93_9f8f_83a0e9bcb3b7_TB5971_11.jpg)
B)![<strong>Find the arc length of the graph of the given equation on the specified interval. y = ( + 1) <sup> </sup> , [2, 5]</strong> A) B) C) D) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_553c_3a94_9f8f_b94c2267ee69_TB5971_11.jpg)
C)![<strong>Find the arc length of the graph of the given equation on the specified interval. y = ( + 1) <sup> </sup> , [2, 5]</strong> A) B) C) D) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_553c_3a95_9f8f_95376977f06b_TB5971_11.jpg)
D)![<strong>Find the arc length of the graph of the given equation on the specified interval. y = ( + 1) <sup> </sup> , [2, 5]</strong> A) B) C) D) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5971/11eaa3e5_553c_3a96_9f8f_41bbf5fd9ef6_TB5971_11.jpg)
( + 1) , [2, 5]
A)
B)
C)
D)
سؤال
Set up, but do not evaluate, an integral for the length of the curve. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Set up, but do not evaluate, an integral for the length of the curve. 
سؤال
Find the length of the curve for the interval 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
Find the length of the curve for the interval 
. 
. سؤال
Find the length of the line segment joining the two given points by finding the equation of the line using Equation (2). Then check your answer by using the distance formula. (0, 0), (1, 8)
A)
B)9
C)
D)
A)
B)9
C)
D)
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ملء الشاشة (f)
Deck 8: Further Applications of Integration
1
A demand curve is given by .
Find the consumer surplus when the selling price is $ .
.Find the consumer surplus when the selling price is $
.
2
The marginal revenue from producing x units of a certain product is (in dollars per unit). Find the increase in revenue if the production level is raised from 1,100 units to units.
A)$
B)$51367000
C)$26866667
D)$17765250
E)$37974583
(in dollars per unit). Find the increase in revenue if the production level is raised from 1,100 units to units.A)$
B)$51367000
C)$26866667
D)$17765250
E)$37974583
$
3
For any normal distribution, find to two decimal places.
to two decimal places.
4
You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)
A)208 lb
B)104 lb
C)1040 lb
D)520 lb
A)208 lb
B)104 lb
C)1040 lb
D)520 lb
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5
The manager of a fast-food restaurant determines that the average time that her customers wait for service is 2 minutes. Find the probability that a customer is served within the first minutes.
A)
B)
C)
D)
E)
minutes.A)
B)
C)
D)
E)
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6
For a given commodity and pure competition, the number of units produced and the price per unit are determined as the coordinates of the point of intersection of the supply and demand curves. Given the demand curve and the supply curve ,
find the consumer surplus.
and the supply curve ,find the consumer surplus.
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7
A hot, wet summer is causing a mosquito population explosion in a lake resort area. The number of mosquitoes is increasing at an estimated rate of per week (where t is measured in weeks). By how much does the mosquito population increase between the 4th and th weeks of summer?
A)5702
B)6702
C)8702
D)7702
E)
per week (where t is measured in weeks). By how much does the mosquito population increase between the 4th and th weeks of summer?A)5702
B)6702
C)8702
D)7702
E)
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8
A movie theater has been charging $ .00 per person and selling about tickets on a typical weeknight. After surveying their customers, the theater estimates that for every $ that they lower the price, the number of moviegoers will increase by per night. Find the demand function and calculate the consumer surplus when the tickets are priced at $ .
.00 per person and selling about tickets on a typical weeknight. After surveying their customers, the theater estimates that for every $ that they lower the price, the number of moviegoers will increase by per night. Find the demand function and calculate the consumer surplus when the tickets are priced at $ . فتح الحزمة
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9
The manager of a fast-food restaurant determines that the average time that her customers wait for service is 2 minutes.
The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than % of her customers. What value of x must she use in the advertisement "if you aren't served within x minutes, you get a free hamburger"?
The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than
% of her customers. What value of x must she use in the advertisement "if you aren't served within x minutes, you get a free hamburger"? فتح الحزمة
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10
Boxes are labeled as containing 500 g of cereal. The machine filling the boxes produces weights that are normally distributed with standard deviation 12
g.If the target weight is 500 g, what is the probability that the machine produces a box with less than g of cereal? Round your answer to four decimal places.
g.If the target weight is 500 g, what is the probability that the machine produces a box with less than
g of cereal? Round your answer to four decimal places. فتح الحزمة
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11
Let
a) For what value of c is f a probability density function?
b) For that value of c, find P (-1 < X < 1).
a) For what value of c is f a probability density function?
b) For that value of c, find P (-1 < X < 1).
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12
If f (x) is the probability density function for the blood cholesterol level of men over the age of 40, where x is measured in milligrams per deciliter, express as an integral the probability that the cholesterol level of such a man lies between 195 and .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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13
Suppose the average waiting time for a customer's call to be answered by a company representative (modeled by exponentially decreasing probability density functions) is minutes. Find the median waiting time.
A) minutes
B) minutes
C) minutes
D) minutes
E) minutes
minutes. Find the median waiting time.A)
minutesB)
minutesC)
minutesD)
minutesE)
minutes فتح الحزمة
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14
You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)
A)332.8 lb
B)1331.2 lb
C)2662.4 lb
D)665.6 lb
A)332.8 lb
B)1331.2 lb
C)2662.4 lb
D)665.6 lb
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15
The demand function for a commodity is given by . Find the consumer surplus when the sales level is .
A)$9458
B)$10458
C)$
D)$8458
E)$4458
. Find the consumer surplus when the sales level is .A)$9458
B)$10458
C)$
D)$8458
E)$4458
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16
A type of lightbulb is labeled as having an average lifetime of hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean µ = . What is the median lifetime of these lightbulbs? Give your answer rounded to two decimal places.
hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean µ = . What is the median lifetime of these lightbulbs? Give your answer rounded to two decimal places. فتح الحزمة
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17
Let the function whose graph is shown be a probability density function. Calculate the mean.
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18
The standard deviation for a random variable with probability density function f and mean µ is defined . Find the standard deviation for an exponential density function with mean .
A)
B)
C)
D)
E)
. Find the standard deviation for an exponential density function with mean .A)
B)
C)
D)
E)
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19
The marginal cost function is defined to be the derivative of the cost function. If the marginal cost of manufacturing x units of a product is (measured in dollars per unit) and the fixed start-up cost is , use the Total Change Theorem to find the cost of producing the first 5,000 units.
A)$35,444,500
B)$
C)$35,434,500
D)$35,454,500
E)$35,484,500
is defined to be the derivative of the cost function. If the marginal cost of manufacturing x units of a product is (measured in dollars per unit) and the fixed start-up cost is , use the Total Change Theorem to find the cost of producing the first 5,000 units.A)$35,444,500
B)$
C)$35,434,500
D)$35,454,500
E)$35,484,500
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20
A gate in an irrigation canal is constructed in the form of a trapezoid ft wide at the bottom, ft wide at the top, and 2 ft high. It is placed vertically in the canal, with the water extending to its top. Find the hydrostatic force on one side of the gate..
A) lb
B) lb
C) lb
D) lb
E)None of these
ft wide at the bottom, ft wide at the top, and 2 ft high. It is placed vertically in the canal, with the water extending to its top. Find the hydrostatic force on one side of the gate..A)
lbB)
lbC)
lbD)
lbE)None of these
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21
The masses are located at the point . Find the moments and and the center of mass of the system. ;
A)
B)
C)
D)
E)
are located at the point . Find the moments and and the center of mass of the system. ; A)
B)
C)
D)
E)
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22
A rectangular tank has width 4 ft, height 4 ft, and length 7 ft. It is filled with equal volumes of water and oil. The oil has a weight density of 50 lb/ft3 and floats on the water. Find the force exerted by the mixture on one end of the tank. (The weight density of water is 62.4 lb/ft3.)
A)1897.6 lb
B)899.2 lb
C)1699.2 lb
D)1798.4 lb
A)1897.6 lb
B)899.2 lb
C)1699.2 lb
D)1798.4 lb
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23
A swimming pool is 10 ft wide and 36 ft long and its bottom is an inclined plane, the shallow end having a depth of ft and the deep end, 12 ft. If the pool is full of water, find the hydrostatic force on the shallow end. (Use the fact that water weighs 62.5 lb/ .)
ft and the deep end, 12 ft. If the pool is full of water, find the hydrostatic force on the shallow end. (Use the fact that water weighs 62.5 lb/ .) فتح الحزمة
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24
Find the center of mass of a lamina in the shape of a quarter-circle with radius with density = .
with density = . فتح الحزمة
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25
Find the centroid of the region shown, not by integration, but by locating the centroids of the
rectangles and triangles and using additivity of moments.
rectangles and triangles and using additivity of moments.
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26
Find the centroid of the region bounded by the graphs of the given equations.
A)
B)
C)
D)
A)
B)
C)
D)
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27
Calculate the center of mass of the lamina with density = .
= . فتح الحزمة
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28
Find the exact coordinates of the centroid.
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29
A trough has vertical ends that are equilateral triangles with sides of length 2 ft. If the trough is filled with water to a depth of 1 ft, find the force exerted by the water on one end of the trough. Round to one decimal place. (The weight density of water is 62.4 lb/ft3.)
A)12.0 lb
B)62.4 lb
C)6.0 lb
D)31.2 lb
A)12.0 lb
B)62.4 lb
C)6.0 lb
D)31.2 lb
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30
A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find the force exerted by the water on the plate. (The weight density of water is 62.4 lb/ft3.) (ft)
A)124.8 lb
B)436.8 lb
C)873.6 lb
D)62.4 lb
(ft)A)124.8 lb
B)436.8 lb
C)873.6 lb
D)62.4 lb
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31
Find the coordinates of the centroid for the region bounded by the curves , x = 0,
and y = .
, x = 0,and y =
. فتح الحزمة
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32
Use the Theorem of Pappus to find the volume of the solid obtained by revolving the region bounded by the graphs of and about the y-axis.
A) 144
B) 108
C) 648
D) 864
and about the y-axis.A) 144
B) 108
C) 648
D) 864
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33
Find the centroid of the region bounded by the curves.
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34
Find the centroid of the region bounded by the given curves.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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35
Find the centroid of the region bounded by the given curves.
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36
You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)
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37
A trough is filled with a liquid of density 855 kg/ . The ends of the trough are equilateral triangles with sides m long and vertex at the bottom. Find the hydrostatic force on one end of the trough.
A)
B)
C)
D)
E)
. The ends of the trough are equilateral triangles with sides m long and vertex at the bottom. Find the hydrostatic force on one end of the trough.A)
B)
C)
D)
E)
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38
An aquarium is 4 ft long, 3 ft wide, and 2 ft deep. If the aquarium is filled with water, find the force exerted by the water (a) on the bottom of the aquarium, (b) on the longer side of the aquarium, and (c) on the shorter side of the aquarium. (The weight density of water is 62.4 lb/ft3.)
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39
Find the centroid of the region bounded by the given curves.
A)
B)
C)
D)
E)None of these
A)
B)
C)
D)
E)None of these
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40
Find the centroid of the region bounded by the graphs of the given equations.
A)
B)
C)
D)
A)
B)
C)
D)
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41
Find the center of mass of the system comprising masses mk located at the points Pk in a coordinate plane. Assume that mass is measured in grams and distance is measured in centimeters.
m1 = 3, m2 = 4, m3 = 5
P1 (-3, 5), P2 (3, 4), P3 (-4, 1)
m1 = 3, m2 = 4, m3 = 5
P1 (-3, 5), P2 (3, 4), P3 (-4, 1)
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42
A cylindrical drum of diameter 2 ft and length 6 ft is lying on its side, submerged in water 16 ft deep. Find the force exerted by the water on one end of the drum to the nearest pound. (The weight density of water is 62.4 lb/ft3.)
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43
Find the volume obtained when the circle of radius with center ( , 0) is rotated about the y-axis.
A)
B)
C)
D)
E)
with center ( , 0) is rotated about the y-axis.A)
B)
C)
D)
E)
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44
Find the centroid of the region bounded by the graphs of and .
and . فتح الحزمة
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45
Find the centroid of the region shown in the figure.
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46
A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find the force exerted by the water on the plate. (The weight density of water is 62.4 lb/ft3.) (ft)
(ft) فتح الحزمة
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47
Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about the x-axis on the interval .
A)
B)
C)
D)
E)
about the x-axis on the interval .A)
B)
C)
D)
E)
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48
You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)
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49
Write an integral giving the area of the surface obtained by revolving the curve about the x-axis. (Do not evaluate the integral.) y = on [3, 6]
A)2
B)2
C)8
D)8
on [3, 6]A)2
B)2
C)8
D)8
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50
Find the area of the surface obtained by rotating the curve about the x-axis.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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51
Find the center of mass of the lamina of the region shown if the density of the circular lamina is five times that of the rectangular lamina.
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52
You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)
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53
A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find the force exerted by the water on the plate. (The weight density of water is 62.4 lb/ft3.) (ft)
(ft) فتح الحزمة
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54
Find the area of the surface obtained by rotating the curve about the y-axis.
A)
B)
C)
D)
E)None of these
A)
B)
C)
D)
E)None of these
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55
Find the area of the surface obtained by revolving the given curve about the x-axis. on
A)
B)
C)
D)
on A)
B)
C)
D)
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56
Find the centroid of the region bounded by the graphs of and .
and . فتح الحزمة
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57
Find the area of the surface obtained by rotating the circle about the line .
A)
B)
C)
D)
E)
about the line .A)
B)
C)
D)
E)
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58
Find the area of the region under the graph of f on [a, b].
A)6
B)-3
C)3
D)-6
A)6
B)-3
C)3
D)-6
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59
Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about the given axis. y-axis
A)
B)
C)
D)
E)
y-axisA)
B)
C)
D)
E)
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60
Find the centroid of the region bounded by the graphs of the given equations.
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61
Use differentials to approximate the arc length of the graph of the equation from P to Q. Round answer to four decimal places. P (3, 12), Q (3.2, 13.24)
A)2.4331
B)1.2166
C)3.6497
D)6.0828
P (3, 12), Q (3.2, 13.24)A)2.4331
B)1.2166
C)3.6497
D)6.0828
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62
Find the arc length function for the curve with starting point .
A)
B)
C)
D)
E)
with starting point .A)
B)
C)
D)
E)
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63
Find the arc length of the graph from A to B.
A) )
B) )
C) )
D) )
A)
)B)
)C)
)D)
) فتح الحزمة
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64
If the infinite curve , is rotated about the x-axis , find the area of the resulting surface.
A)
B)
C)
D)
E)
, is rotated about the x-axis , find the area of the resulting surface.A)
B)
C)
D)
E)
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65
Find the length of the curve.
A)
B)
C)
D)
E)None of these
A)
B)
C)
D)
E)None of these
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66
Find the area of the surface obtained by revolving the given curve about the y-axis.
x = on [0, 2]
x =
on [0, 2] فتح الحزمة
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67
Find the length of the curve.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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68
Find the area of the surface obtained by revolving the graph of y = on [0, 1] about the x-axis.
on [0, 1] about the x-axis. فتح الحزمة
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69
Set up, but do not evaluate, an integral for the length of the curve.
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70
Set up, but do not evaluate, an integral that represents the length of the curve.
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71
Use Simpson's Rule with n = 6 to estimate the length of the curve , . Round your answer to six decimal places.
A)6.987208
B)6.972089
C)6.947582
D)6.947368
E)None of these
, . Round your answer to six decimal places.A)6.987208
B)6.972089
C)6.947582
D)6.947368
E)None of these
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72
Find the area of the surface obtained by revolving the given curve about the x-axis. on [0, 1]
on [0, 1] فتح الحزمة
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73
Find the length of the curve.
A)36.05
B)13.05
C)
D)25.05
E)None of these
A)36.05
B)13.05
C)
D)25.05
E)None of these
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74
Find the area of the surface obtained by rotating the curve about the -axis.
-axis. فتح الحزمة
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75
Find the arc length of the graph of the given equation on the specified interval. y = ( + 1)
, [2, 5]
A)
B)
C)
D)
( + 1) , [2, 5]
A)
B)
C)
D)
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76
Set up, but do not evaluate, an integral for the length of the curve.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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77
Set up, but do not evaluate, an integral for the length of the curve.
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78
Find the length of the curve for the interval .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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79
Find the length of the curve for the interval .
. فتح الحزمة
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80
Find the length of the line segment joining the two given points by finding the equation of the line using Equation (2). Then check your answer by using the distance formula. (0, 0), (1, 8)
A)
B)9
C)
D)
A)
B)9
C)
D)
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