   Chapter 14.1, Problem 21E

Chapter
Section
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 0101y2(x+y)dxdy.

Formula used:

Integration of xn is given as,

xndx=xn+1n+1+C

Calculation:

Consider the function,

0101y2(x+y)dxdy

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

0101y2(x+y)dxdy=01[x22+xy]01y2dy=01(1y22+y1y2)dy=1201dy1201y2dy+01y1y2dy

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

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