   Chapter 7.8, Problem 13E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Evaluating a Double Integral In Exercises 11-24, evaluate the double integral. See ∫ − 3 2 ∫ − 2 4 x y   d x   d y

To determine

To calculate: The double integration 3224(xy)dxdy.

Explanation

Given Information:

The provided integration is 3224(xy)dxdy.

Formula used:

If a binary function F(x,y) is integrable in domain of axb and cyd, the double integration cdabF(x,y)dxdy can be calculated as follows procedure,

Integrate with respect to x by holding y constant,

cdabF(x,y)dxdy=cd[f(x,y)]abdy

Here, function f(x,y) is partial integration of F(x,y) with respect to x variable.

Now, replace the x by limit of integration,

cd[f(x,y)]abdy=cd[f(b,y)f(a,y)]dy

Integrate with respect to x,

cd[f(b,y)f(a,y)]dy=[h(b,y)h(a,y)]cd

Here, the function h(x,b) and is partial integration of f(x,b) with respect to x variable, the function h(x,a) is partial integration of f(x,a) with respect to x variable.

Now, replace the x by limit of integration,

[h(b,y)h(a,y)]cd=[h(b,d)h(b,c)h(a,d)+h(a,c)]

The double integration cdabF(x,y)dydx is [h(b,d)h(b,c)h(a,d)+h(a,c)]

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