Chapter 14.6, Problem 6E

### 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 a Triple Iterated Integral In Exercises 3-10, evaluate the triple iterated integral. ∫ 0 9 ∫ 0 y / 3 ∫ 0 y 2 − 9 x 2 z   d z   d x   d y

To determine

To calculate: The value of triple iterated integral 090y30y29x2zdzdxdy.

Explanation

Given:

The integral is âˆ«09âˆ«0y3âˆ«0y2âˆ’9x2zâ€‰dzdxdy.

Formula used:

Use the formula âˆ«xmdx=xm+1m+1; where m is a constant value except for âˆ’1.

Calculation:

The integral can be calculated as,

âˆ«09âˆ«0y3âˆ«0y2âˆ’9x2zdzdxdy=âˆ«09âˆ«0y3(z22)0y2âˆ’9x2dxdy=âˆ«09âˆ«0y3(y2âˆ’9x22âˆ’02)dxdy=âˆ«0912(y2xâˆ’9x33)0y3dy=âˆ«0912(

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