Chapter 14.1, Problem 20E

### 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

# Evaluating an Iterated Integral In Exercises 11-28, evaluate the iterated integral. ∫ − 4 4 ∫ 0 x 2 64 − x 3   d y   d x

To determine

To calculate: The value of the iterated integral, 440x264x3dydx.

Explanation

Given:

The iterated integral is âˆ«âˆ’44âˆ«0x264âˆ’x3dydx.

Formula used:

Integration of xn is given as,

âˆ«xndx=xn+1n+1+C

Calculation:

Consider the function,

âˆ«âˆ’44âˆ«0x264âˆ’x3dydx

Integrate the function first with respect to x and then with respect to y as,

âˆ«âˆ’44âˆ«0x264âˆ’x3dydx=âˆ«âˆ’44[y64âˆ’x3]0x2dx=âˆ«âˆ’44x264âˆ’x3dx

Put 64âˆ’x3=u and differentiate both sides with respect to x as,

âˆ’3x2dx=dux2dx=âˆ’13du

When x=âˆ’4. Then the value of u,

u=64âˆ’(âˆ’4)3=64âˆ’(âˆ’64)=128

When x=4

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