Chapter 15.7, Problem 18E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use cylindrical coordinates.

**18**. Evaluate
*E* is enclosed by the paraboloid *z* = *x*^{2} + *y*^{2} and the plane *z* = 4.

To determine

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

Explanation

**Given:**

The function is

The region *E* is enclosed by the paraboloid

**Formula used:**

If
*E* given by

If
*z*, then,

The cylindrical coordinates

**Calculation:**

Solve the given equations,

It is observed that *r* varies from 0 to 2,
*z* varies from

Use the equation (2) to integrate and apply the limit values

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