Chapter 15.5, Problem 7E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the area of the surface.

**7**. The part of the hyperbolic paraboloid *z = y*^{2} – *x*^{2} that lies between the cylinders *x*^{2} *+ y*^{2} = 1 and *x*^{2} + *y*^{2} = 4

To determine

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

Explanation

**Given:**

The function is the part of the hyperbolic paraboloid

The region *D* lies between the cylinders

**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 1 to 2 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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