Chapter 5: Q 20. (page 451)
Consider the integral
(a) Solve this integral by using integration by substitution with u = tan x.
(b) Solve this integral another way, by using integration by substitution with u = sec x.
Short Answer
(a)
(b)
Chapter 5: Q 20. (page 451)
Consider the integral
(a) Solve this integral by using integration by substitution with u = tan x.
(b) Solve this integral another way, by using integration by substitution with u = sec x.
(a)
(b)
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Suppose . Calculate and compare the values of the following definite integrals:
role="math" localid="1648786835678"
Explain why, if , then is if and is if . Your explanation should include a discussion of domains and absolute values.
Solve each of the integrals in Exercises 39–74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
Find three integrals in Exercises 21–70 in which the denominator of the integrand is a good choice for a substitution u(x).
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