Chapter 14.1, Problem 22E

### 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 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 âˆ«02âˆ«3y2âˆ’6y2yâˆ’y23ydxdy.

Formula used:

Integration of xn is given as,

âˆ«xndx=xn+1n+1+C

Calculation:

Consider the function,

âˆ«02âˆ«3y2âˆ’6y2yâˆ’y23ydxdy

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

âˆ«02âˆ«3y2âˆ’6y2yâˆ’y23ydxdy=3âˆ«02[xy]3y2âˆ’6y2yâˆ’y2dy=3âˆ«02[y(2yâˆ’y2)âˆ’y(3y2âˆ’6y)

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