   Chapter 10.5, Problem 69E

Chapter
Section
Textbook Problem

Finding the Area of a Surface of Revolution In Exercises 69 and 70, use the integration capabilities of a graphing utility to approximate the area of the surface formed by revolving the polar equation over the given interval about the polar axis. r = 4 cos 2 θ ,       [ 0 , π 4 ]

To determine

To calculate: The area of surface formed by revolving the polar equation over the given interval about the polar axis by using the integration capabilities of graphing utility.

Explanation

Given:

Polar equation is given r=4cos2θ and the interval 0θπ4 and the axis of revolution is polar axis.

Formula Used:

s=2παβf(θ)sinθ(f(θ))2+(f(θ))2dθ

Calculation:

Given polar equation is r=4cos2θ where interval is 0θπ4 and the axis of revolution is polar axis

It is known that area of surface will be given by below formula:

s=2παβf(θ)sinθ(f(θ))2+(f(θ))2dθ

And r=4cos2θ,α=0,β=π4

And

drdθ=f(θ

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