   Chapter 15.6, Problem 1E

Chapter
Section
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=0103xz2dzdx=0103xz2dzdx

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

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