   Chapter 14.1, Problem 22E

Chapter
Section
Textbook Problem

Evaluating an Iterated Integral In Exercises 11-28, evaluate the iterated integral. ∫ 0 2 ∫ 3 y 2 − 6 y 2 y − y 2 3 y   d x   d y

To determine

To calculate: The value of the iterated integral, 023y26y2yy23ydxdy.

Explanation

Given:

The iterated integral is 023y26y2yy23ydxdy.

Formula used:

Integration of xn is given as,

xndx=xn+1n+1+C

Calculation:

Consider the function,

023y26y2yy23ydxdy

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

023y26y2yy23ydxdy=302[xy]3y26y2yy2dy=302[y(2yy2)y(3y26y)

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