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8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781285741550

Chapter 8.2, Problem 17E

Textbook Problem

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The given curve is rotated about the *y*-axis. Find the area of the resulting surface.

**17**.
*y* ≤ *a* / 2

To determine

**To find:** The area of the surface obtained by rotating the curve about *y*-axis.

**Given information:**

The equation of the curve is

The curve is bounded between

**Calculation:**

Show the equation of the curve.

Calculate the area of the surface obtained by rotating the curve about *y*-axis using the relation:

Here, *S* is the area of the surface obtained by rotating the curve about *y*-axis.

Differentiate both sides of Equation (1) with respect to *y*.

Substitute *x*, 0 for *a,* and *b* in Equation (2)

Calculus: Early Transcendentals

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