Chapter 14.5, Problem 18E

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11th Edition

Ron Larson + 1 other

ISBN: 9781337275347

Textbook Problem

Finding Surface Area In Exercises 17-20, find the area of the surface.

The portion of the paraboloid

To determine

**To calculate:** The area of the surface given that is given in the question as

Explanation

**Given:**

The region is denoted by

**Formula Used:**

The surface area of the region *R* can be calculated by,

Apply the power rule of integration, that is,

The differentiation formula is

The equation of the circle is *r* represents the radius.

**Calculation:**

The given function is written as

Now, on performing partial differentiation on it with respect to *x*, make sure to use the formula,

Now, with respect to *y*.

The following can be found,

Substitute the calculated value in the formula

For the given region, the limits need to be converted to polar points in case of both *x* and *y*.

Then, the polar curve,

Since the region is in the first octant, the obtained region can be described as,

The region is, then, bounded by

Thus, on applying limits to the integral using the formula

We obtain the following,

On substituting

We get

Perform integration on

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