Chapter 15.5, Problem 9E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the area of the surface.

**9**. The part of the surface z = *xy* that lies within the cylinder *x*^{2}* + y*^{2}* =* 1

To determine

**To find:** The area of given surface.

Explanation

**Given:**

The part of the surface

The region *D* lies within the cylinder

**Formula used:**

The surface area with equation

Here, *D* is the given region.

If *R* given by

If

**Calculation:**

Convert the given problems into the polar coordinates to make the problem easier. By given the conditions, it is observed that, *r* varies from 0 to 1 and

Obtain the partial derivatives of *f* with respect to *x* and *y*.

Then, by the equation (1), the area of surface is given by,

Use the equation (2) to separate the integrals and substitute

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