   Chapter 14.2, Problem 16E

Chapter
Section
Textbook Problem

Evaluating a Double IntegralIn Exercises 13–20, set up integrals for both orders of integration. Use the more convenient order to evaluate the integral over the plane region R . ∫ R ∫ x e y   d A R: triangle bounded by y = 4 − x , y = 0 , x = 0

To determine

To calculate: The integral RxeydA over the plane region R: triangle bounded by y=4x,y=0 and x=0.

Explanation

Given:

The integral, RxeydA

R: triangle bounded by y=4x,y=0 and x=0.

Calculation:

Consider the integral RxeydA where,

R: triangle bounded by y=4x,y=0 and x=0.

The region is sketched as,

Provided integral can be written in these orders of integration:

RxeydA=y=04x=04yxeydxdy

And,

RxeydA=x=04y=04xxeydydx

Here, because of the ease it provides, second integral form has been used to solve

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