   Chapter 15.6, Problem 3E

Chapter
Section
Textbook Problem

Evaluate the iterated integral.3. ∫ 0 2 ∫ 0 z 2 ∫ 0 y   −   z   ( 2 x   − y )   d x   d y   d z

To determine

To evaluate: The given iterated integral.

Explanation

Given:

The function is f(x,y,z)=2xy .

The region is B={(x,y,z)|0x(yz),0yz2,0z2} .

Calculation:

The given integral is, 020z20yz(2xy)dxdydz .

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

020z20yz(2xy)dxdydz=020z2(2x22yx)0yzdydz=020z2[(yz)2y(yz)]dydz=020z2[(yz)(yzy)]dydz=020z2[(yz)(z)]dydz

=020z2[(z2yz)]dydz

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

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