Stewart – Calculus ET 8e Chapter 7 Form A
1. Evaluate the integral.
2. Evaluate the integral.
3. Evaluate the following integral.
4. Evaluate the integral to six decimal places.
5. Evaluate the integral.
6. Make a substitution to express the integrand as a rational function and then evaluate the integral.
Round the answer to four decimal places.
7. Use the Table of Integrals to evaluate the integral to three decimal places.
Stewart – Calculus ET 8e Chapter 7 Form A
8. Use the Table of Integrals to evaluate the integral.
9. Use the Trapezoidal Rule to approximate for . Round the result to four decimal
places.
10. Determine whether the integral converges or diverges. If it converges, find its value.
11. Find the integral.
12. Evaluate the integral using an appropriate trigonometric substitution.
13. Find the integral.
14. The region under the graph of
on the interval [1, 2] is revolved about the x-axis. Find the volume of the resulting solid.
15. Evaluate the integral.
Stewart – Calculus ET 8e Chapter 7 Form A
16. Use (a) the Trapezoidal Rule and (b) Simpson’s Rule to approximate the integral to four decimal
places. Compare your results with the exact value.
17. Eight milligrams of a dye are injected into a vein leading the an individual’s heart. The
concentration of dye in the aorta (in milligrams per liter) measured at 2-sec intervals is shown in
the accompanying table. Use Simpson’s Rule with and the formula
to estimate the person’s cardiac output, where D is the quantity of dye injected in milligrams,
is the concentration of the dye in the aorta, and R is measured in liters per minute. Round to one
decimal place.
t 0 2 4 6 8 10 12 14 16 18 20 22 24
C(t) 0 0 2.6 6.3 9.7 7.5 4.5 3.5 2.2 0.6 0.3 0.1 0
18. Find a bound on the error in approximating the integral using (a) the Trapezoidal Rule and
(b) Simpson’s Rule with subintervals.
19. A body moves along a coordinate line in such a way that its velocity at any time t, where ,
is given by
.
Find its position function if it is initially located at the origin.
20. Determine whether the improper integral converges or diverges, and if it converges, find its value.
Stewart – Calculus ET 8e Chapter 7 Form A
Answer Key
Stewart – Calculus ET 8e Chapter 7 Form B
1. Evaluate the integral.
2. Evaluate the integral.
3. Evaluate the integral.
4. Evaluate the integral.
5. Find the area bounded by the curves and between and .
6. Evaluate the integral using the indicated trigonometric substitution.
7. Evaluate the integral to six decimal places.
8. Find the volume of the resulting solid if the region under the curve
from to is rotated about the x-axis. Round your answer to four decimal places.
Stewart – Calculus ET 8e Chapter 7 Form B
9. Make a substitution to express the integrand as a rational function and then evaluate the integral.
Round the answer to four decimal places.
10. Evaluate the integral.
11. Evaluate the integral.
12. Evaluate the integral.
13. Evaluate the integral.
14. Estimate the area of the shaded region by using the Trapezoidal Rule with . Round the
answer to the nearest tenth.
Stewart – Calculus ET 8e Chapter 7 Form B
15. Evaluate the integral or show that it is divergent.
16. Evaluate the integral using an appropriate trigonometric substitution.
17. Find the integral using an appropriate trigonometric substitution.
18. Evaluate the integral.
19. Find the integral.
20. Find a bound on the error in approximating the integral using (a) the Trapezoidal Rule and
(b) Simpson’s Rule with subintervals.
Stewart – Calculus ET 8e Chapter 7 Form B
Answer Key
Stewart – Calculus ET 8e Chapter 7 Form C
Select the correct answer for each question.
____ 1. Evaluate the integral.
a.
b.
c.
d.
e.
____ 2. Evaluate the integral using integration by parts with the indicated choices of u and dv.
a.
b.
c.
d.
e.
____ 3. Evaluate the integral.
a.
b.
c.
d.
Stewart – Calculus ET 8e Chapter 7 Form C
____ 4. Find the integral.
a.
b.
c.
d.
____ 5. Evaluate the integral.
a.
b.
c.
d.
e. None of these
Stewart – Calculus ET 8e Chapter 7 Form C
____ 6. Find the average value of the function in the interval .
a.
b.
c.
d.
e.
____ 7. A particle moves on a straight line with velocity function . Find its position function
.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 7 Form C
____ 8. Use long division to evaluate the integral.
a.
b.
c.
d.
e.
____ 9. Find the integral.
a.
b.
c.
d.
Stewart – Calculus ET 8e Chapter 7 Form C
____ 10. Find the integral.
a.
b.
c.
d.
____ 11. Find the integral.
a.
b.
c.
d.
Stewart – Calculus ET 8e Chapter 7 Form C
____ 12. Use a table of integrals to evaluate the integral.
a.
b.
c.
d.
____ 13. Use long division to evaluate the integral.
The choices are rounded to 3 decimal places.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 7 Form C
____ 14. Evaluate the integral.
a.
b.
c.
d.
e.
____ 15. Use a table of integrals to evaluate the integral.
a.
b.
c.
d.
Stewart – Calculus ET 8e Chapter 7 Form C
____ 16. Use a table of integrals to evaluate the integral.
a.
b.
c.
d.
____ 17. Evaluate the integral or show that it is divergent.
a.
b.
c.
d.
5
4
e.
Stewart – Calculus ET 8e Chapter 7 Form C
____ 18. Determine whether the improper integral converges or diverges, and if it converges, find its value.
a.
15
b.
15
2
c. Diverges
d.
15
2
____ 19. Let a and b be real numbers. What integral must appear in place of the question mark ”?” to make
the following statement true?
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 7 Form C
____ 20. Evaluate the integral.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 7 Form C
Answer Key
Stewart – Calculus ET 8e Chapter 7 Form D
Select the correct answer for each question.
____ 1. Find the integral.
a.
b.
c.
d.
____ 2. Evaluate the integral.
a.
b. 6.5700
c. 0.7166
d. 11.8665
e.
____ 3. Evaluate the integral using integration by parts with the indicated choices of u and dv.
a.
b.
c.
d.
e.