Chapter 14.1, Problem 19E

### 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. ∫ 0 1 ∫ 0 x 1 − x 2 d y   d x

To determine

To calculate: The value of the iterated integral 010x1x2dydx.

Explanation

Given:

Theintegral is

âˆ«01âˆ«0x1âˆ’x2dydx

Formula used:

âˆ«xndx=xn+1n+1+C

Calculation:

We will use the following rule of integration:

âˆ«xndx=xn+1n+1+C

where C is integration constant.

Now we see,

âˆ«01âˆ«0x1âˆ’x2dydx=âˆ«01[y1âˆ’x2]0xdx=âˆ«01x1âˆ’x2dx....................(a)

Let us substitute 1âˆ’x2=u.

Differentiating both sides with respect to x, we get,

âˆ’2xdx=duxdx=âˆ’12du

When x=0, then u=1âˆ’0=1

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