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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 integral in Example 1, integrating first with respect to y, then z, and then x.

EXAMPLE 1 Evaluate the triple integral B x y z 2 d v , where B is the rectangular box given by

B = { ( x , y , z ) | 0 x 1 , 1 y 2 , 0 z 3 }

To determine

To evaluate: The integral in example 1, by changing the order of integration.

Explanation

Given:

The function is f(x,y,z)=xyz2 .

The region is B={(x,y,z)|0x1,1y2,0z3}

Calculation:

The given integral with required order is, Bxyx2dV=010312xyz2dydzdx .

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

Bxyx2dV=0103xz2[y22]12dzdx=0103xz2[(2)22(1)22]dzdx=0103xz2[412]dzdx=0103xz2[32]dzdx

Integrate the above integral with respect to z and apply the limit

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Chapter 15 Solutions

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