Chapter 14.1, Problem 21E

### 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 1 − y 2 ( x + y )     d x   d y

To determine

To calculate: The value of the iterated integral, 0101y2(x+y)dxdy.

Explanation

Given:

The iterated integral is âˆ«01âˆ«01âˆ’y2(x+y)dxdy.

Formula used:

Integration of xn is given as,

âˆ«xndx=xn+1n+1+C

Calculation:

Consider the function,

âˆ«01âˆ«01âˆ’y2(x+y)dxdy

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

âˆ«01âˆ«01âˆ’y2(x+y)dxdy=âˆ«01[x22+xy]01âˆ’y2dy=âˆ«01(1âˆ’y22+y1âˆ’y2)dy=12âˆ«01dyâˆ’12âˆ«01y2dy+âˆ«01y1âˆ’y2dy

Put, 1âˆ’y2=u and differentiate both sides with respect

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started