   Chapter 7.8, Problem 31E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding Area with a Double Integral In Exercises 31-36, use a double integral to find the area of the region bounded by the graphs of the equations. See Example 4. y = 9 − x 2 ,     y = 0

To determine

To calculate: The area of the region bounded by graphs of equation y=9x2 and y=0 by using double integration.

Explanation

Given Information:

The provided equations are y=9x2 and y=0.

Formula used:

If a region is R defined in the domain of ayb and cxd, then,

The area of the region R is,

A=cdabdydx

Calculation:

Consider the graphs of equation,

y=9x2 and y=0

The graph of region bounded by y=9x2 and y=0 shown in below.

The bounds for x are 3x3 and bounds for y are 0y9x2.

The area of the region is

A=3309x2dydx

Integrate with respect to y by holding x constant,

3309x2dydx=33[y]09

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