   Chapter 7.8, Problem 16E ### 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 ∫ 0 1 ∫ 0 y ( 6 x + 5 y 3 ) d x   d y

To determine

To calculate: The double integration 010y(6x+5y2)dxdy.

Explanation

Given Information:

The provided integration is 010y(6x+5y3)dxdy.

Formula used:

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

Integrate with respect to y by holding x constant,

cdabF(x,y)dydx=cd[f(x,y)]abdx

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,

cd[f(x,y)]abdx=cd[f(x,b)f(x,a)]dx

Integrate with respect to x,

cd[f(x,b)f(x,a)]dx=[h(x,b)h(x,a)]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

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