   Chapter 15, Problem 29RE

Chapter
Section
Textbook Problem

Calculate the value of the multiple integral.29. ∭ E x y   d V , where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, 0 ≤ z ≤ x + y

To determine

To calculate: The given triple integral.

Explanation

Given:

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

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

Calculation:

First compute the integral with respect to z and apply the limit.

ExydV=030x0x+yxydzdydx=030x[xyz]0x+ydydx=030x[xy(x+y0)]dydx=030x(x2y+xy2)dydx

Compute the integral with respect to y and apply the limit

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