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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.

9. D e y 2 d A , D = { ( x , y ) | 0 y 3 , 0 x y }

To determine

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

Explanation

Given

The domain is, D={(x,y)|0y3,0xy} .

Calculation:

First, compute the integral with respect to x.

Dey2dA=03[0yey2dx]dy=03[xey2]0ydy

Apply the limit value for x,

Dey2dA=03[ey2(y)(0)ey2]dy=03[ey2y]dy

Compute the integral with respect to y.

Let t=y2

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