Chapter 14, Problem 19RE

### 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

# Finding VolumeIn Exercises 17–20, use a double integral to find the volume of the indicated solid.

To determine

To calculate: The volume of the solid bounded by z=4x2y2, 1x1 and 1y1 by double integration for the region shown below

Explanation

Given:

The function is z=4âˆ’x2âˆ’y2.

The diagram given is:

Formula used:

The volume of a solid when z=f(x,y) is providedby

V=âˆ«x1x2âˆ«y1y2f(x,y)dydx

Using the integration formula,

âˆ«xndx=xn+1n+1

Calculation:

Apply the limits and given function f(x,y)=4âˆ’x2âˆ’y2 in the formula of volume:

âˆ«âˆ’11âˆ«âˆ’11(4âˆ’x2âˆ’y2)dydx=âˆ«âˆ’11[4yâˆ’x2yâˆ’y33]âˆ’11dx=

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