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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Evaluate the double integral.

20. D x y d A , D is enclosed by the quarter-circle y = 1 x 2 , x 0 , and the axes

To determine

To calculate: The value of given double integral over D .

Explanation

Given

The function is f(x,y)=xy .

The domain D is enclosed by the quarter circle y=1x2,x0 and the axes.

Calculation:

First, compute the integral with respect to y.

DxydA=01[01x2xydy]dx=01[y2x2]01x2dx

Apply the limit value for y,

DxydA=01[x(1x2)22x(0)22]dx=12

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Chapter 15 Solutions

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