   Chapter 10, Problem 109RE

Chapter
Section
Textbook Problem

# Finding the Arc Length of a Polar Curve In Exercises 109 and 110, find the length of the curve over the given interval. Polar Equation Interval r   =   5 cos θ [ π 2 ,   π ]

To determine

To calculate: The length of the curve given as, r=5cosθ over the interval, [π2,π].

Explanation

Given:

The polar equation is;

r=5cosθ

And interval is [π2,π].

Formula used:

The length of the graph of r=f(θ) from θ=α to θ=β is given by;

s=αβr2+(drdθ)2dθ

Calculation:

Consider the given polar equation,

r=5cosθ

Now, find the derivative with respect to θ as shown;

drdθ=ddθ(5cosθ)=5sinθ

Then, the length of the curve over the interval [π2,π] is;

s=π2πr2+(drdθ)2dθ=π2π(5cosθ)2+(5sinθ)2<

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