Chapter 15, Problem 32RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Calculate the value of the multiple integral.

**32**.
*E* is bounded by the planes *y* = 0, *z* = 0, *x* + *y* = 2 and the cylinder *y*^{2} + *z*^{2} = 1 in the first octant

To determine

**To calculate:** The given triple integral.

Explanation

**Given:**

The function is

The region *E* is bounded by the planes

**Calculation:**

Solve the given equations as follows.

And

From the above equations, it is observed that *x* varies from 0 to
*y* varies from 0 to 1 and *z* varies from 0 to
*x* and apply the limit.

Compute the integral with respect to *z* and apply the limit

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