Chapter 8.4, Problem 3E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Using Trigonometric Substitution In Exercises 3–6, find the indefinite integral using the substitution x = 4 sin θ . ∫ 1 ( 16 − x 2 ) 3 / 2 d x

To determine
The solution of the indefinite integral 1(16x2)3/2dx.

Explanation

Given: The indefinite integral âˆ«1(16âˆ’x2)3/2dx.

Explanation: Because 116âˆ’x2 is of the form 1a2âˆ’x2, use the trigonometric substitution: x=4sinÎ¸ ==> dx=4cosÎ¸dÎ¸. Hence, âˆ«1(16âˆ’x2)3/2dx=âˆ«1(16âˆ’x2)3dx=âˆ«

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