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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Evaluate the triple integral.

9. E y d V , where E = { ( x , y , z ) | 0 x 3 , 0 y x , x y z x + y }

To determine

To evaluate: The integral of EydV.

Explanation

Given:

The function is f(x,y,z)=y.

The region is E={(x,y,z)|0x3,0yx,xyzx+y}.

Calculation:

The given integral is, EydV=030xxyx+yydzdydx.

Integrate the given integral with respect to z and apply the limit of it.

EydV=030xy[z]xyx+ydydx=030xy[(x+y)(xy)]dydx=030xy[2y]dydx=030xy2dydx

Integrate the given integral with respect to y and apply the limit

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Chapter 15 Solutions

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