Chapter 5: Q 91. (page 431)
Prove the integration formula.
(a) by applying integration by parts to .
(a) by differentiating.
Short Answer
Part (a). The solution is .
Part (b). The solution is.
Chapter 5: Q 91. (page 431)
Prove the integration formula.
(a) by applying integration by parts to .
(a) by differentiating.
Part (a). The solution is .
Part (b). The solution is.
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Why is it okay to use a triangle without thinking about the unit circle when simplifying expressions that result from a trigonometric substitution withor ? Why do we need to think about the unit circle after trigonometric substitution with ?
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.
Solve given definite integral.
Explain why, if , then is if and is if . Your explanation should include a discussion of domains and absolute values.
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