   Chapter 15, Problem 32RE

Chapter
Section
Textbook Problem

Calculate the value of the multiple integral.32. ∭ E z   d V , where E is bounded by the planes y = 0, z = 0, x + y = 2 and the cylinder y2 + z2 = 1 in the first octant

To determine

To calculate: The given triple integral.

Explanation

Given:

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

The region E is bounded by the planes y=0,z=0,x+y=2 and the cylinder y2+z2=1 in the first octant.

Calculation:

Solve the given equations as follows.

x+y=2x=2y

And

y2+z2=1z2=1y2z=1y2

From the above equations, it is observed that x varies from 0 to 2y , y varies from 0 to 1 and z varies from 0 to 1y2 . First compute the integral with respect to x and apply the limit.

EzdV=0101y202yzdxdzdy=0101y2[xz]02ydzdy=0101y2[z(2y0)]dzdy=0101y2(2zyz)dzdy

Compute the integral with respect to z and apply the limit

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Convert to whole or mixed numbers. 1255

Contemporary Mathematics for Business & Consumers

Sometimes, Always, or Never: If c is a critical number, then f′(c) = 0.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

True or False: The function f is continuous at (0, 0), where

Study Guide for Stewart's Multivariable Calculus, 8th 