LEARNING GOAL: to identify an appropriate trigonometric substitution used to evaluate an integral containin

an a² - r², a² + r², or a²-a² term using the structure of known trigonometric identities.

5. Write a substitution equation, corresponding differential, and trigonometric identity used initially to evaluate

each of the following integrals.

2²

(a) √ (9-22)3/2 d

(b)

2²

(x² +16)³/2°

dr

(c) 2√/9²-25

(d) [.

(e)

dy

(1 - 4y²)3/2

dz

2²√/36 +2²

da

dz

)

J (52²-4)3/2

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