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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Using Geometry Use a geometric argument to show that 0 3 0 9 y 2 9 x 2 y 2 d x d y = 9 π 2

To determine

To prove: That 0309x29x2y2dxdy=9π2 with the help of a geometric argument.

Explanation

Given:

0309x29x2y2dxdy=9π2

Formula used:

The following formula is used to calculate the volume of a sphere:

(43)πr3

Double integral formula

Proof:

It is to be proved that 0309x29x2y2dxdy=9π2 is true.

It is known that z=9x2y2 is a half sphere centered about the origin having radius 3.

In the x-y plane, x=9y2 is a half circle with radius 3, 0y3 eliminates the negative portion after applying the limits of integration

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Chapter 14 Solutions

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