Chapter 15.5, Problem 14E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your calculator to estimate the integral.

**14**. The part of the surface z = cos(*x*^{2} +*y*^{2}) that lies inside the cylinder *x*^{2} + *y*^{2} = 1

To determine

**To find:** The area of given surface correct to four decimal places by using integrating calculator.

Explanation

**Given:**

The function,

The region *D* lies inside the cylinder

**Formula used:**

The surface area with equation *D* is the given region.

If *f* is a polar rectangle *R* given by

If *x* and *y* then,

**Calculation:**

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

The partial derivatives

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

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