   Chapter 7.8, Problem 34E ### 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. x + y = 2 ,     x = 0 ,   y = 0

To determine

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

Explanation

Given Information:

The provided equations are x+y=2 and x=0,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,

x+y=2 and x=0,y=0.

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

Solve the equation x+y=2 for y.

y=2xy=(2x)2

The bounds for x are 0x4 and bounds for y are 0y(2x)2.

The area of the region is

A=040(2x)2dydx

Integrate with respect to y by holding x constant,

040(2x)2dydx=04[y]0(2

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