Chapter 8.2, Problem 33E

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Chapter
Section

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

# If the curve y = f(x), a ≤ x ≤ b, is rotated about the horizontal line y = c, where f(x) ≤ c, find a formula for the area of the resulting surface.

To determine

To find: The formula for the area of resulting surface when the curve is rotated about horizontal line y=c .

Explanation

Given information:

The given curve is y=f(x) , the range x is between aâ‰¤xâ‰¤b

The curve is rotated about the horizontal line y=c

Calculation:

Show the expression for surface area obtained when the curve is rotated about x axis.

S=âˆ«ab2Ï€|f(x)|1+{dydx}2dx (1)

The distance from y=c to any point (x,f(x)) is |f(x)âˆ’c| , when f(xâ‰¤c),|f(x)âˆ’c<

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