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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.

17. D x cos y d A , D is bounded by y = 0. y = x2, x = 1

To determine

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

Explanation

Given

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

The domain D is bounded by y=x,y=x2,x=1 .

Calculation:

First, compute the integral with respect to y.

DxcosydA=01[0x2xcosydy]dx=01[xsiny]0x2dx

Apply the limit value for y,

DxcosydA=01[xsin(x2)xsin0]dx=01xsinx2dx

Compute the integral with respect to x. for that substitute, t=x2dt=2xdx

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Chapter 15 Solutions

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