   Chapter 14, Problem 15RE

Chapter
Section
Textbook Problem

Evaluating a Double Integral In Exercises 15 and 16, set up integrals for both orders of integration. Use the more convenient order to evaluate the integral over the plane ∫ R ∫ 4 x y   d A R: rectangle with vertices (0, 0), (0, 4), (2, 4), (2, 0)

To determine

To calculate: The expression of the integral R4xydA for both orders. Also, use more convenient order to find the value of the integral.

Explanation

Given:

The integral R4xydA.

And,

R: rectangle with vertices (0, 0), (0, 4), (2, 4), (2, 0).

Formula used:

The area of a region is given by

A=xlxhylyhdydx

Use the integration formula:

xndx=xn+1n+1

Calculation:

Plot the given rectangle:

From the graph, if dA=dxdy then double integral will be:

0402(4xy)dxdy

If dA=dydx, then double integral will be:

0204(4xy)dydx

Since, both the expressions are convenient to use

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