Chapter 15.7, Problem 21E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use cylindrical coordinates.

**21**. Evaluate
^{2}*dV*, where *E* is the solid that lies within the cylinder .*x*^{2} + y* ^{2}* = l, above the plane

To determine

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

Explanation

**Given:**

The function is

The region *E* lies within the cylinder

**Formula used:**

If
*E* given by

The cylindrical coordinates

**Calculation:**

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

Use the formula mentioned above to change the given problem into cylindrical coordinates. Then, by the equation (1), the value of the given triple integral is obtained as follows.

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

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