تكلم مع الذكاء الاصطناعي
Deck 6: Applications of the Integral
ملء الشاشة (f)
سؤال
Find the area of the shaded region bounded by the graphs of 
and 
and the 
axis. 
and and the axis. 
سؤال
Find the volume of the solid shown in the figure if the radius of the upper circle is 
, the radius of the bottom circle is 
and the height of the solid is 
. 
, the radius of the bottom circle is and the height of the solid is . سؤال
Find the area of the region enclosed by the curves 
and 
. 
and . سؤال
The base of a solid is the region bounded by the 
-axis and the semi-ellipse 
Each cross section perpendicular to the base and parallel to the 
-axis is an isosceles triangle whose height is twice its base. Find the volume of this solid. 
-axis and the semi-ellipse Each cross section perpendicular to the base and parallel to the -axis is an isosceles triangle whose height is twice its base. Find the volume of this solid. سؤال
Find the area of the shaded region below which is bounded by the graphs of 
and 
. 
and . سؤال
Calculate the area of the region enclosed by 
and 
for 
. 
and for . سؤال
Find the area of the region shown in the figure. Use symmetry to facilitate your computation. 
سؤال
Find the area of the region bounded by the graphs of 
and 
and the y-axis. 
and and the y-axis. سؤال
Find the area of the region bounded by 
and 
for 
. 
and for . سؤال
Find the mass of a rod of length 2 with density function 
, where 
is the distance from one of the rod's ends. 
, where is the distance from one of the rod's ends. سؤال
Find the mass of a semicircular disc of radius 
for which the density function is 
, where 
is the distance from the diameter. 
for which the density function is , where is the distance from the diameter. سؤال
Find the area enclosed by the graphs 
and 
.
and . سؤال
Let 
. Find an equation for 
in the interval 
such that 
is equal to the average of 
on 
. Use Newton's Method with 
. Give your answer to three decimal places.
. Find an equation for in the interval such that is equal to the average of on . Use Newton's Method with . Give your answer to three decimal places. سؤال
Calculate the total area between the graphs of the functions 
and 
.
and . سؤال
Find the area of the region bounded by the graphs of 
and 
. 
and . سؤال
Find the area of the shaded region below which is bounded by the graphs of 
and 
. 
and . سؤال
Find the area of the region bounded by the graphs of the functions 
and 
.
and . سؤال
Find the area of the shaded region shown in the figure. 
سؤال
Find the volume of the solid whose base is the semi-circular region 
and the cross sections perpendicular to the y-axis are isosceles right triangles whose hypotenuse lie on the base of the solid. 
and the cross sections perpendicular to the y-axis are isosceles right triangles whose hypotenuse lie on the base of the solid. سؤال
Find the area of the region bounded by the graphs of 
and 
.
and . سؤال
Compute the volume of the solid whose base is the region between the x-axis and the curve 
over 
, and the cross sections parallel to the y-axis and perpendicular to the base are semicircles. 
over , and the cross sections parallel to the y-axis and perpendicular to the base are semicircles. سؤال
Find the mass of the solid whose base is the region inside the unit circle 
, and the cross sections parallel to the x-axis and perpendicular to the base are semicircles whose diameters are on the base.
The density function is
. 
, and the cross sections parallel to the x-axis and perpendicular to the base are semicircles whose diameters are on the base.The density function is
. سؤال
Calculate the population within a 2-mile radius of a city center if the radial population density is 
thousands per square mile.
thousands per square mile. سؤال
Find the volume of the solid obtained by revolving the region 
about the line 
. 
about the line . سؤال
Calculate the population within a 2-mile radius of a city center if the radial population density is 
thousands per square mile.
thousands per square mile. سؤال
A solid circular cylinder of radius 
and length 
whose density is the square of the distance from the axis of symmetry has the following mass:
A)
.
B)
.
C)
.
D)
.
E)
.
and length whose density is the square of the distance from the axis of symmetry has the following mass:A)
.B)
.C)
.D)
.E)
. سؤال
Compute the volume of the solid whose base is the region between the x-axis and the curve 
over 
, and the cross sections parallel to the y-axis and perpendicular to the base are squares. 
over , and the cross sections parallel to the y-axis and perpendicular to the base are squares. سؤال
The volume of the solid obtained by rotating the ellipse 
about the y-axis is 
A)
B)
C)
D)
E) none of the above.
about the y-axis is A)
B)
C)
D)
E) none of the above.
سؤال
Find the value of 
in 
such that 
is equal to the average of 
on 
where 
.
in such that is equal to the average of on where . سؤال
Find the mass of a rod of length 
aligned on the positive 
-axis if its mass density 
equals the area of the right triangle shown in the figure. 
aligned on the positive -axis if its mass density equals the area of the right triangle shown in the figure. سؤال
Find a value 
in 
such that 
is equal to the average of 
on 
if 
in such that is equal to the average of on if سؤال
Find the volume of the solid obtained by revolving the region 
about the x-axis. 
about the x-axis. سؤال
Find the volume of the solid obtained by rotating the region 
about the line 
. 
about the line . سؤال
Find the volume generated by revolving the triangle shown in the figure about side 
. 
. سؤال
Find the volume generated by revolving a right triangle with angle 
and hypotenuse 2 about a line perpendicular to the hypotenuse passing through the vertex of the 
angle, as shown in the figure. 
and hypotenuse 2 about a line perpendicular to the hypotenuse passing through the vertex of the angle, as shown in the figure. سؤال
The volume of the ice goblet obtained by rotating the region shown in the figure about the y-axis is 
A)
.
B)
.
C)
.
D)
.
E)
.
A)
.B)
.C)
.D)
.E)
. سؤال
Calculate the population within a 4-mile radius of a city center if the radial population density is 
thousands per square mile.
thousands per square mile. سؤال
What is the average volume of a regular tetrahedron with side 
if 
varies from 1 to 4? 
if varies from 1 to 4? سؤال
Find the volume of the solid obtained by revolving the region in the first quadrant between the curves 
and 
about the line 
. 
and about the line . سؤال
Find the value of 
in 
such that 
is equal to the average of 
on 
.
in such that is equal to the average of on . سؤال
Find the volume of the solid obtained by rotating the region shown in the figure about the line 
. 
. سؤال
The volume of the solid obtained by rotating the region shown in the figure about the y-axis is 
A)
.
B)
.
C)
.
D)
.
E) none of the above.
A)
.B)
.C)
.D)
.E) none of the above.
سؤال
Find the volume of the solid obtained by rotating the region 
about the line 
. 
about the line . سؤال
Find the volume of the solid obtained by rotating the region between the curve 
and the x-axis above the interval 
about the line 
. 
and the x-axis above the interval about the line . سؤال
Find the volume of the solid obtained by rotating the region between the curves 
and 
about the line 
. Use the formula 
. 
and about the line . Use the formula . سؤال
Find the volume of the solid obtained by rotating the region in the first quadrant enclosed by the curves 
and 
for 
, about the line 
. 
and for , about the line . سؤال
Use the Shell Method to find the volume of the solid obtained by rotating the region shown in the figure about the y-axis. 
سؤال
Use the Shell Method to calculate the volume of the solid obtained by rotating the region shown in the figure about the line 
. 
. سؤال
Find the volume generated by revolving an isosceles right triangle with hypotenuse 2 about a line perpendicular to the hypotenuse passing through the vertex of one of the acute angles. 
سؤال
The volume of the solid obtained by revolving the region between the lines 
and 
about the y-axis is 
A)
.
B)
.
C)
.
D)
.
E)
.
and about the y-axis is A)
.B)
.C)
.D)
.E)
. سؤال
Find the volume of the solid generated by revolving the region below 
over 
about the line 
. 
over about the line . سؤال
Use the Shell Method to calculate the volume of the solid obtained by rotating the region shown in the figure about the line 
. 
. سؤال
Use the Shell Method to calculate the volume of the solid obtained by rotating the region 
about the line 
. 
about the line . سؤال
To compute the volume of the solid obtained by rotating the region shown in the figure about the y-axis, the most convenient method is 
A) the Disk Method.
B) the Disk Method in addition to the Shell Method.
C) the Shell Method.
D) Integration by Parts.
E) none of these methods.
A) the Disk Method.
B) the Disk Method in addition to the Shell Method.
C) the Shell Method.
D) Integration by Parts.
E) none of these methods.
سؤال
Find the volume generated by revolving the triangle shown in the figure about a line parallel to the hypotenuse, passing through the vertex of the right angle. 
سؤال
To compute the volume of the solid obtained by rotating the region between the line 
and the curve 
in the first quadrant about the y-axis, the most convenient method is 
A) the Shell Method.
B) the Disk Method.
C) the Shell Method in addition to the Disk Method.
D) Integration by Parts.
E) none of these methods.
and the curve in the first quadrant about the y-axis, the most convenient method is A) the Shell Method.
B) the Disk Method.
C) the Shell Method in addition to the Disk Method.
D) Integration by Parts.
E) none of these methods.
سؤال
Calculate the volume of the solid obtained by rotating the region between the curves 
and 
over 
about the line 
. 
and over about the line . سؤال
Use the Shell Method to calculate the volume of the solid obtained by rotating the region shown in the figure about the y-axis. 
سؤال
Use the Shell Method to calculate the volume of the solid obtained by rotating the region shown in the figure about the y-axis. 
سؤال
Use the Shell Method to calculate the volume of the solid obtained by rotating the sector shown in the figure about the line 
Use the formula 
. 
Use the formula . سؤال
Find the approximate work required to pump water out of the container shown in the figure if the container is filled with water to the top of the cylinder. The density of water is 
. 
. سؤال
Find the work required to build a pyramid of height 
, whose base is an isosceles right triangle with a leg length of 
. The pyramid will be built with stones of density 
. 
A)
B)
C)
D)
E)
, whose base is an isosceles right triangle with a leg length of . The pyramid will be built with stones of density . A)
B)
C)
D)
E)
سؤال
To compute the volume of the solid obtained by rotating the region in the figure about the y-axis, the most convenient method is 
A) the Disk Method.
B) the Shell Method.
C) both the Disk and Shell Methods.
D) Integration by Parts.
E) none of these methods.
A) the Disk Method.
B) the Shell Method.
C) both the Disk and Shell Methods.
D) Integration by Parts.
E) none of these methods.
سؤال
Find the work required to move an object along the x-axis from 
to 
by the force 
.
to by the force . سؤال
A conical container (vertex down) is filled to half of its height with liquid of density 
. The radius of the conical container is 
and its height is 
, measured in meters.
The approximate work required to pump the liquid out of the top of the tank is
A)
B)
C)
D)
E) none of the above.
. The radius of the conical container is and its height is , measured in meters.The approximate work required to pump the liquid out of the top of the tank is
A)
B)
C)
D)
E) none of the above.
سؤال
The vertical tank shown in the figure is half full of water. Given that the density of water is 
, the approximate work required to empty the tank by pumping the water out through an outlet at the top of the tank is 
A)
B)
C)
D)
E) none of the above.
, the approximate work required to empty the tank by pumping the water out through an outlet at the top of the tank is A)
B)
C)
D)
E) none of the above.
سؤال
A vertical tank, with elliptic horizontal cross section 
and height 
is full of water. The work done in pumping the water out through an outlet at the top of the tank is which of the following? (Assume that the water weighs 62.5 pounds per cubic foot.) 
A)
B)
C)
D)
E) None of the above.
and height is full of water. The work done in pumping the water out through an outlet at the top of the tank is which of the following? (Assume that the water weighs 62.5 pounds per cubic foot.) A)
B)
C)
D)
E) None of the above.
سؤال
Calculate the volume of the solid obtained by rotating the region shown in the figure about the line 
. 
. سؤال
Find the work done in moving an object from 
to 
by the force 
.
to by the force . سؤال
The volume of the solid obtained by rotating the region shown in the figure about the
Y-axis is
A)
.
B)
.
C)
.
D)
.
E)
.
Y-axis is
A)
.B)
.C)
.D)
.E)
. سؤال
Use the Shell Method to calculate the volume of the solid obtained by rotating the region shown in the figure about the line 
. 
. سؤال
The work (against gravity) required to build a right pyramid of height 
, with equilateral triangle base of side length 
, using stones of density 
is 
A)
.
B)
.
C)
.
D)
.
E) none of the above.
, with equilateral triangle base of side length , using stones of density is A)
.B)
.C)
.D)
.E) none of the above.
سؤال
If 
Joules of work are needed to stretch a spring 
cm beyond equilibrium, the spring constant 
is
A)
.
B)
.
C)
.
D)
.
E)
.
Joules of work are needed to stretch a spring cm beyond equilibrium, the spring constant isA)
.B)
.C)
.D)
.E)
. سؤال
سؤال
A chain weighing 25 pounds per foot is hanging from the top of a 100-foot building, as shown in the figure. Find the work needed to pull the chain to the top of the building. 
سؤال
Calculate the volume of the solid obtained by rotating the region in the figure about the y-axis. (Note: the x and y scales are different.) 
سؤال
Find the work done in moving an object from 
to 
by the force 
.
to by the force . سؤال
Find the work done in moving an object from 
to 
by the force 
.
to by the force . سؤال
To compute the volume of the solid obtained by rotating the region shown in the figure about the y-axis, the most convenient method is 
A) the Disk Method.
B) the Shell Method.
C) the Disk and Shell Methods.
D) Integration by Parts.
E) none of these methods.
A) the Disk Method.
B) the Shell Method.
C) the Disk and Shell Methods.
D) Integration by Parts.
E) none of these methods.
سؤال
Use the Shell Method to find the volume of the solid obtained by rotating the region shown in the figure about the line 
. 
. 
فتح الحزمة
قم بالتسجيل لفتح البطاقات في هذه المجموعة!
Unlock Deck
Unlock Deck
1/80
العب
ملء الشاشة (f)
Deck 6: Applications of the Integral
1
Find the area of the shaded region bounded by the graphs of and and the axis.
and and the axis. 
2
Find the volume of the solid shown in the figure if the radius of the upper circle is , the radius of the bottom circle is and the height of the solid is .
, the radius of the bottom circle is and the height of the solid is . 
3
Find the area of the region enclosed by the curves and .
and . 
4
The base of a solid is the region bounded by the -axis and the semi-ellipse Each cross section perpendicular to the base and parallel to the -axis is an isosceles triangle whose height is twice its base. Find the volume of this solid.
-axis and the semi-ellipse Each cross section perpendicular to the base and parallel to the -axis is an isosceles triangle whose height is twice its base. Find the volume of this solid. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
5
Find the area of the shaded region below which is bounded by the graphs of and .
and . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
6
Calculate the area of the region enclosed by and for .
and for . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
7
Find the area of the region shown in the figure. Use symmetry to facilitate your computation.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
8
Find the area of the region bounded by the graphs of and and the y-axis.
and and the y-axis. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
9
Find the area of the region bounded by and for .
and for . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
10
Find the mass of a rod of length 2 with density function , where is the distance from one of the rod's ends.
, where is the distance from one of the rod's ends. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
11
Find the mass of a semicircular disc of radius for which the density function is , where is the distance from the diameter.
for which the density function is , where is the distance from the diameter. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
12
Find the area enclosed by the graphs and .
and . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
13
Let . Find an equation for in the interval such that is equal to the average of on . Use Newton's Method with . Give your answer to three decimal places.
. Find an equation for in the interval such that is equal to the average of on . Use Newton's Method with . Give your answer to three decimal places. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
14
Calculate the total area between the graphs of the functions and .
and . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
15
Find the area of the region bounded by the graphs of and .
and . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
16
Find the area of the shaded region below which is bounded by the graphs of and .
and . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
17
Find the area of the region bounded by the graphs of the functions and .
and . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
18
Find the area of the shaded region shown in the figure.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
19
Find the volume of the solid whose base is the semi-circular region and the cross sections perpendicular to the y-axis are isosceles right triangles whose hypotenuse lie on the base of the solid.
and the cross sections perpendicular to the y-axis are isosceles right triangles whose hypotenuse lie on the base of the solid. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
20
Find the area of the region bounded by the graphs of and .
and . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
21
Compute the volume of the solid whose base is the region between the x-axis and the curve over , and the cross sections parallel to the y-axis and perpendicular to the base are semicircles.
over , and the cross sections parallel to the y-axis and perpendicular to the base are semicircles. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
22
Find the mass of the solid whose base is the region inside the unit circle , and the cross sections parallel to the x-axis and perpendicular to the base are semicircles whose diameters are on the base.
The density function is .
, and the cross sections parallel to the x-axis and perpendicular to the base are semicircles whose diameters are on the base.The density function is
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
23
Calculate the population within a 2-mile radius of a city center if the radial population density is thousands per square mile.
thousands per square mile. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
24
Find the volume of the solid obtained by revolving the region about the line .
about the line . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
25
Calculate the population within a 2-mile radius of a city center if the radial population density is thousands per square mile.
thousands per square mile. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
26
A solid circular cylinder of radius and length whose density is the square of the distance from the axis of symmetry has the following mass:
A) .
B) .
C) .
D) .
E) .
and length whose density is the square of the distance from the axis of symmetry has the following mass:A)
.B)
.C)
.D)
.E)
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
27
Compute the volume of the solid whose base is the region between the x-axis and the curve over , and the cross sections parallel to the y-axis and perpendicular to the base are squares.
over , and the cross sections parallel to the y-axis and perpendicular to the base are squares. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
28
The volume of the solid obtained by rotating the ellipse about the y-axis is
A)
B)
C)
D)
E) none of the above.
about the y-axis is A)
B)
C)
D)
E) none of the above.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
29
Find the value of in such that is equal to the average of on where .
in such that is equal to the average of on where . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
30
Find the mass of a rod of length aligned on the positive -axis if its mass density equals the area of the right triangle shown in the figure.
aligned on the positive -axis if its mass density equals the area of the right triangle shown in the figure. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
31
Find a value in such that is equal to the average of on if
in such that is equal to the average of on if فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
32
Find the volume of the solid obtained by revolving the region about the x-axis.
about the x-axis. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
33
Find the volume of the solid obtained by rotating the region about the line .
about the line . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
34
Find the volume generated by revolving the triangle shown in the figure about side .
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
35
Find the volume generated by revolving a right triangle with angle and hypotenuse 2 about a line perpendicular to the hypotenuse passing through the vertex of the angle, as shown in the figure.
and hypotenuse 2 about a line perpendicular to the hypotenuse passing through the vertex of the angle, as shown in the figure. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
36
The volume of the ice goblet obtained by rotating the region shown in the figure about the y-axis is
A) .
B) .
C) .
D) .
E) .
A)
.B)
.C)
.D)
.E)
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
37
Calculate the population within a 4-mile radius of a city center if the radial population density is thousands per square mile.
thousands per square mile. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
38
What is the average volume of a regular tetrahedron with side if varies from 1 to 4?
if varies from 1 to 4? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
39
Find the volume of the solid obtained by revolving the region in the first quadrant between the curves and about the line .
and about the line . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
40
Find the value of in such that is equal to the average of on .
in such that is equal to the average of on . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
41
Find the volume of the solid obtained by rotating the region shown in the figure about the line .
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
42
The volume of the solid obtained by rotating the region shown in the figure about the y-axis is
A) .
B) .
C) .
D) .
E) none of the above.
A)
.B)
.C)
.D)
.E) none of the above.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
43
Find the volume of the solid obtained by rotating the region about the line .
about the line . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
44
Find the volume of the solid obtained by rotating the region between the curve and the x-axis above the interval about the line .
and the x-axis above the interval about the line . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
45
Find the volume of the solid obtained by rotating the region between the curves and about the line . Use the formula .
and about the line . Use the formula . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
46
Find the volume of the solid obtained by rotating the region in the first quadrant enclosed by the curves and for , about the line .
and for , about the line . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
47
Use the Shell Method to find the volume of the solid obtained by rotating the region shown in the figure about the y-axis.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
48
Use the Shell Method to calculate the volume of the solid obtained by rotating the region shown in the figure about the line .
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
49
Find the volume generated by revolving an isosceles right triangle with hypotenuse 2 about a line perpendicular to the hypotenuse passing through the vertex of one of the acute angles.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
50
The volume of the solid obtained by revolving the region between the lines and about the y-axis is
A) .
B) .
C) .
D) .
E) .
and about the y-axis is A)
.B)
.C)
.D)
.E)
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
51
Find the volume of the solid generated by revolving the region below over about the line .
over about the line . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
52
Use the Shell Method to calculate the volume of the solid obtained by rotating the region shown in the figure about the line .
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
53
Use the Shell Method to calculate the volume of the solid obtained by rotating the region about the line .
about the line . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
54
To compute the volume of the solid obtained by rotating the region shown in the figure about the y-axis, the most convenient method is
A) the Disk Method.
B) the Disk Method in addition to the Shell Method.
C) the Shell Method.
D) Integration by Parts.
E) none of these methods.
A) the Disk Method.
B) the Disk Method in addition to the Shell Method.
C) the Shell Method.
D) Integration by Parts.
E) none of these methods.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
55
Find the volume generated by revolving the triangle shown in the figure about a line parallel to the hypotenuse, passing through the vertex of the right angle.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
56
To compute the volume of the solid obtained by rotating the region between the line and the curve in the first quadrant about the y-axis, the most convenient method is
A) the Shell Method.
B) the Disk Method.
C) the Shell Method in addition to the Disk Method.
D) Integration by Parts.
E) none of these methods.
and the curve in the first quadrant about the y-axis, the most convenient method is A) the Shell Method.
B) the Disk Method.
C) the Shell Method in addition to the Disk Method.
D) Integration by Parts.
E) none of these methods.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
57
Calculate the volume of the solid obtained by rotating the region between the curves and over about the line .
and over about the line . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
58
Use the Shell Method to calculate the volume of the solid obtained by rotating the region shown in the figure about the y-axis.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
59
Use the Shell Method to calculate the volume of the solid obtained by rotating the region shown in the figure about the y-axis.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
60
Use the Shell Method to calculate the volume of the solid obtained by rotating the sector shown in the figure about the line Use the formula .
Use the formula . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
61
Find the approximate work required to pump water out of the container shown in the figure if the container is filled with water to the top of the cylinder. The density of water is .
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
62
Find the work required to build a pyramid of height , whose base is an isosceles right triangle with a leg length of . The pyramid will be built with stones of density .
A)
B)
C)
D)
E)
, whose base is an isosceles right triangle with a leg length of . The pyramid will be built with stones of density . A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
63
To compute the volume of the solid obtained by rotating the region in the figure about the y-axis, the most convenient method is
A) the Disk Method.
B) the Shell Method.
C) both the Disk and Shell Methods.
D) Integration by Parts.
E) none of these methods.
A) the Disk Method.
B) the Shell Method.
C) both the Disk and Shell Methods.
D) Integration by Parts.
E) none of these methods.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
64
Find the work required to move an object along the x-axis from to by the force .
to by the force . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
65
A conical container (vertex down) is filled to half of its height with liquid of density . The radius of the conical container is and its height is , measured in meters.
The approximate work required to pump the liquid out of the top of the tank is
A)
B)
C)
D)
E) none of the above.
. The radius of the conical container is and its height is , measured in meters.The approximate work required to pump the liquid out of the top of the tank is
A)
B)
C)
D)
E) none of the above.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
66
The vertical tank shown in the figure is half full of water. Given that the density of water is , the approximate work required to empty the tank by pumping the water out through an outlet at the top of the tank is
A)
B)
C)
D)
E) none of the above.
, the approximate work required to empty the tank by pumping the water out through an outlet at the top of the tank is A)
B)
C)
D)
E) none of the above.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
67
A vertical tank, with elliptic horizontal cross section and height is full of water. The work done in pumping the water out through an outlet at the top of the tank is which of the following? (Assume that the water weighs 62.5 pounds per cubic foot.)
A)
B)
C)
D)
E) None of the above.
and height is full of water. The work done in pumping the water out through an outlet at the top of the tank is which of the following? (Assume that the water weighs 62.5 pounds per cubic foot.) A)
B)
C)
D)
E) None of the above.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
68
Calculate the volume of the solid obtained by rotating the region shown in the figure about the line .
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
69
Find the work done in moving an object from to by the force .
to by the force . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
70
The volume of the solid obtained by rotating the region shown in the figure about the
Y-axis is
A) .
B) .
C) .
D) .
E) .
Y-axis is
A)
.B)
.C)
.D)
.E)
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
71
Use the Shell Method to calculate the volume of the solid obtained by rotating the region shown in the figure about the line .
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
72
The work (against gravity) required to build a right pyramid of height , with equilateral triangle base of side length , using stones of density is
A) .
B) .
C) .
D) .
E) none of the above.
, with equilateral triangle base of side length , using stones of density is A)
.B)
.C)
.D)
.E) none of the above.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
73
If Joules of work are needed to stretch a spring cm beyond equilibrium, the spring constant is
A) .
B) .
C) .
D) .
E) .
Joules of work are needed to stretch a spring cm beyond equilibrium, the spring constant isA)
.B)
.C)
.D)
.E)
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
74
A vertical cylindrical tank of radius 5 feet and height 12 feet is full of water. The water weighs 62.5 pounds per cubic foot. Find the work done in pumping out the water:
A) through an outlet at the top of the tank.
B) through an outlet 6 feet above the top of the tank.
A) through an outlet at the top of the tank.
B) through an outlet 6 feet above the top of the tank.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
75
A chain weighing 25 pounds per foot is hanging from the top of a 100-foot building, as shown in the figure. Find the work needed to pull the chain to the top of the building.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
76
Calculate the volume of the solid obtained by rotating the region in the figure about the y-axis. (Note: the x and y scales are different.)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
77
Find the work done in moving an object from to by the force .
to by the force . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
78
Find the work done in moving an object from to by the force .
to by the force . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
79
To compute the volume of the solid obtained by rotating the region shown in the figure about the y-axis, the most convenient method is
A) the Disk Method.
B) the Shell Method.
C) the Disk and Shell Methods.
D) Integration by Parts.
E) none of these methods.
A) the Disk Method.
B) the Shell Method.
C) the Disk and Shell Methods.
D) Integration by Parts.
E) none of these methods.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
80
Use the Shell Method to find the volume of the solid obtained by rotating the region shown in the figure about the line .
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
فتح الحزمة
k this deck
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 80 في هذه المجموعة.
