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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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.

4 x ( x y 3 + 4 y 2 ) d y

To determine

To calculate: The partial integration 4x(xy3+4y2)dy.

Explanation

Given Information:

The integration is 4x(xy3+4y2)dy.

Formula used:

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

Integrate with respect to y by holding x constant,

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

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

Now, replace the y by limit of integration,

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

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

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