Deck 5: Integrals

Question 1

The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car. 0 0
60 10 70 20 80 30 90 40 100 50

A)1.8 miles
B)0.6 miles
C)0.8 miles
D)1.2 miles
E)2.4 miles

Answer 1

1.2 miles

Question 2

Find the derivative of the function.

Answer 2

Question 3

Evaluate the integral.

A)
B)
C)
D)
E)

Answer 3

Question 4

Use the Midpoint Rule with n = 5 to approximate the integral. Round your answer to three decimal places.

A)
B)
C)
D)
E)

Question 5

Evaluate the integral.

A)
B)
C)
D)
E)

Question 6

The velocity function (in meters per second) is given for a particle moving along a line. Find the distance traveled by the particle during the given time interval.

A)68 m
B)100 m
C)64 m
D)36 m
E)72 m

Question 7

Evaluate the Riemann sum for with four subintervals, taking the sample points to be right endpoints.

A)
B)
C)
D)
E)

Question 8

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

A)
B)
C)
D)
E)

Question 9

Evaluate the definite integral.

Question 10

Evaluate the integral.

A)
B)
C)
D)
E)

Question 11

Find the average value of the function on the given interval.

A)
B)
C)
D)
E)

Question 12

Evaluate the integral by making the given substitution.

A)
B)
C)
D)
E)

Question 13

Evaluate the indefinite integral.

A)
B)
C)
D)
E)

Question 14

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

A)
B)
C)
D)
E)none of these

Question 15

The area of the region that lies to the right of the y-axis and to the left of the parabola (the shaded region in the figure) is given by the integral .Find the area..

A)
B)
C)
D)
E)

Question 16

Evaluate the indefinite integral.

A)
B)
C)
D)
E)

Question 17

Evaluate the definite integral.

Question 18

Find a function such that for x > 0 and some number
a.

Question 19

Evaluate the indefinite integral.

Question 20

The acceleration function (in m/ ) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval.

A)
B)
C)
D)
E)

Question 21

Evaluate by interpreting it in terms of areas.

Question 22

The velocity graph of a car accelerating from rest to a speed of 7 km/h over a period of 10 seconds is shown. Estimate to the nearest integer the distance traveled during this period. Use a right sum with .

Question 23

Evaluate by interpreting it in terms of areas.

Question 24

Use the Midpoint Rule with n = 10 to approximate the integral.

A)
B)
C)
D)
E)

Question 25

If and , find .

A)
B)
C)
D)
E)

Question 26

Determine a region whose area is equal to .

A)
B)
C)
D)
E)

Question 27

The velocity graph of a braking car is shown. Use it to estimate to the nearest foot the distance traveled by the car while the brakes are applied.Use a left sum with n = 7.

Question 28

Given that , find .

Question 29

Express the integral as a limit of sums. Then evaluate the limit.

Question 30

A table of values of an increasing function is shown. Use the table to find an upper estimate of . -45 -37 -27 9 10 23

Question 31

Evaluate by interpreting it in terms of areas.

Question 32

The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find a lower estimate for the distance that she traveled during these three seconds. 2.8
3.5
6.9
8.2
12.2
16.3

Question 33

By reading values from the given graph of , use five rectangles to find a lower estimate, to the nearest whole number, for the area from 0 to 10 under the given graph of .