470 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
8.4 Trigonometric Substitution
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the indefinite integral by making the substitution .
a.
b.
c.
d.
e.
____ 2. Find the indefinite integral by making the substitution .
a.
b.
c.
d.
e.
8.4 Trigonometric Substitution 471
____ 3. Find the indefinite integral by making the substitution .
a.
b.
c.
d.
e.
____ 4. Find the indefinite integral by making the substitution .
a.
b.
c.
d.
e.
472 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 5. Find the indefinite integral by making the substitution .
a.
b.
c.
d.
e.
____ 6. Find the indefinite integral by making the substitution .
a.
b.
c.
d.
e.
8.4 Trigonometric Substitution 473
____ 7. Find the indefinite integral by making the substitution .
a.
b.
c.
d.
e.
____ 8. Find the indefinite integral by making the substitution .
a.
b.
c.
d.
e.
474 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 9. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 10. Find .
a.
b.
c.
d.
e.
8.4 Trigonometric Substitution 475
____ 11. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 12. Find the indefinite integral.
a.
b.
c.
d.
e.
476 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
____ 13. Find .
a.
b.
c.
d.
e.
____ 14. Complete the square and find .
a.
b.
c.
d.
e.
8.4 Trigonometric Substitution 477
____ 15. Evaluate the integral using the integration limits. Round your answer
to three decimal places.
a.
b.
c.
d.
e.
____ 16. Find the definite integral.
a.
b.
c.
d.
e.
478 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
8.4 Trigonometric Substitution
Answer Section