   Chapter 7.8, Problem 8E ### 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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# Finding Partial Integrals In Exercises 1-10, find the partial integral. See Example 1. ∫ − 1 − y 2 1 − y 2 ( x 2 + y 2 ) d x

To determine

To calculate: The partial integration 1y21y2(x2+y2)dx.

Explanation

Given Information:

The integration is 1y21y2(x2+y2)dx.

Formula used:

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

Integrate with respect to x by holding y constant,

abF(x,y)dx=[f(x,y)]ab

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,

[f(x,y)]ab=[f(a,y)f(b,y)]

The double integration abF(x,y)dx is [f(a,y)f(b,y)].

Calculation:

Consider the polynomial,

1y21y2(x2+y2)dx

Integrate with respect to x by holding y constant,

1y21y2(x2+y2)dx=[x33

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