   Chapter 14.2, Problem 14E

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 ∫ sin x sin y   d A R: rectangle with vertices ( − π , 0 ) , ( π , 0 ) , ( π , π / 2 ) , ( − π , π / 2 )

To determine

To calculate: The integral RsinxsinydA over the plane region R rectangle with vertices (π,0),(π,0),(π,π2) and (π,π2).

Explanation

Given:

The integral, RsinxsinydA

R: rectangle with vertices (π,0),(π,0),(π,π2) and (π,π2).

Calculation:

As provided the integral, RsinxsinydA where,

R: rectangle with vertices (π,0),(π,0),(π,π2) and (π,π2).

The region can be sketched as,

Provided integral can be written in these orders of integration:

RsinxsinydA=y=0π2x=ππsinxsinydxdy

And,

R<

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