Chapter 15.7, Problem 20E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use cylindrical coordinates.

**20**. Evaluate
*E* is the solid that lies between the cylinders *x*^{2} + y^{2} = 1 and .*x*^{2} + *y*^{2} = 16, above the *xy*-plane, and below the plane *z = y +* 4.

To determine

**To evaluate:** The given triple integral by using cylindrical coordinates.

Explanation

**Given:**

The function is

The region *E* lies between the cylinders
*xy* plane and below the plane

**Formula used:**

If
*E* given by

The cylindrical coordinates

**Calculation:**

From the given conditions, it is observed that *r* varies from 1 to 4,
*z* varies from 0 to

Integrate with respect to *z* and apply the limit of it.

On further simplification, the value of triple integral becomes,

Integrate with respect to

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