Chapter 15, Problem 38RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the volume of the given solid.

**38.** Bounded by the cylinder *x*^{2} + *y*^{2} = 4 and the planes *z* = 0 and *y* + *z* = 3

To determine

**To find:** The volume of the given solid.

Explanation

**Given:**

The region *E* is bounded by the cylinder

**Formula used:**

The volume of the given solid is given by,

If
*E* given by

**Calculation:**

Since equation of the cylinder is given, it is much easier to use cylindrical coordinates. From the given conditions, it is observed that *r* varies from 0 to 2, *z* varies from 0 to

Integrate with respect to *z* and apply the limit

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