   Chapter 14.1, Problem 20E

Chapter
Section
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 440x264x3dydx.

Formula used:

Integration of xn is given as,

xndx=xn+1n+1+C

Calculation:

Consider the function,

440x264x3dydx

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

440x264x3dydx=44[y64x3]0x2dx=44x264x3dx

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

3x2dx=dux2dx=13du

When x=4. Then the value of u,

u=64(4)3=64(64)=128

When x=4

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