1. If the expression x³√√9x² – 1 occurs in an integral, which trigonometric substitution will you use?

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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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For No. 1 and 2, explain why you got that answer. For No. 3, show your complete solution neatly and legibly using two methods.

1. If the expression x³√√9x² - 1 occurs in an integral, which trigonometric
substitution will you use?
a.) x = 3 sin 0
b.) x = = ²3 sin 0
c.) x = 3 sec 0
1
d.) x = = sec 0
2. What transformation/manipulation can be done to the integrand to solve
dx
S
? Do not evaluate. [Hint: Complete the square in the radicand to
√x²+2x+5
make it look like any of the three expressions where trigonometric
substitution is appropriate.]
-3√3
3. Evaluate £³√³
x
√36-x² dx in two ways (by algebraic substitution or by
Chain Rule for Integrals and by trigonometric substitution).
Transcribed Image Text:1. If the expression x³√√9x² - 1 occurs in an integral, which trigonometric substitution will you use? a.) x = 3 sin 0 b.) x = = ²3 sin 0 c.) x = 3 sec 0 1 d.) x = = sec 0 2. What transformation/manipulation can be done to the integrand to solve dx S ? Do not evaluate. [Hint: Complete the square in the radicand to √x²+2x+5 make it look like any of the three expressions where trigonometric substitution is appropriate.] -3√3 3. Evaluate £³√³ x √36-x² dx in two ways (by algebraic substitution or by Chain Rule for Integrals and by trigonometric substitution).
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