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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.

22. D y d A , D is the triangular region with vertices (0, 0), (1, 1), and (4, 0)

To determine

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

Explanation

Given

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

The domain D is a triangle whose vertices are (0,0),(1,1),(4,0) .

Calculation:

The equation of the sides of the triangle are x=y and x=43y .

First, compute the integral with respect to x.

DydA=01[y43yydx]dy=01[yx]y43ydy

Apply the limit value for x,

DydA=01[y(43y)y(y)]dy=01(4y3y2y2)dy=

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Chapter 15 Solutions

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