Chapter 15.7, Problem 19E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use cylindrical coordinates.

**19**. Evaluate
*E* is the solid in the first octant that lies under the paraboloid *z* = 4 – *x*^{2}– *y*^{2}.

To determine

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

Explanation

**Given:**

The function is

The region *E* lies under the paraboloid

**Formula used:**

If
*E* given by

The cylindrical coordinates

**Calculation:**

Solve the given equation

Therefore, *r* varies from 0 to 2. Since the given lies in the first octant,
*z* varies from 0 to

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

Integrate with respect to

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