   Chapter 15.2, Problem 9E

Chapter
Section
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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