   Chapter 7.8, Problem 33E ### 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. 2 x − 3 y = 0 ,   x + y = 5 ,   y = 0

To determine

To calculate: The area of the region bounded by graphs of equation  2x3y=0, x+y=5, and  y=0 by using double integration.

Explanation

Given Information:

The provided equations are  2x3y=0, x+y=5, 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 equations,

2x3y=0, x+y=5, and  y=0.

The graph of region bounded by  2x3y=0, x+y=5, and  y=0 is shown in below.

The bounds for x are 32yxy+5 and bounds for y are 0y2.

The area of the region is

A=0232yy+5dxdy

Integrate with respect to x by holding y constant,

0232yy+5dxdy=

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