   Chapter 10.5, Problem 58E

Chapter
Section
Textbook Problem

Finding the Arc Length of a Polar Curve In Exercises 53-58, find the length of the curve over the given interval. r = 8 ( 1 + cos θ ) ,       [ 0 , π 3 ]

To determine

To calculate: The length of curve the polar equation r=8(1+cosθ) in the interval [0,π3].

Explanation

Given:

The polar equation is r=8(1+cosθ) and the interval is [0,π3].

Formula Used:

Length of curve of polar coordinates

s=βαr2+(drdθ)2dθ

Here, s is arc length of polar region is, r is distance from the origin of the curve. α And β are the intervals and r=f(θ).

d(cosx)dx=sinx, d(a)dx=0, sin2θ+cos2θ=1, cos2θ=2tanθ1+tan2θ And (a)dx=ax here ‘a’ is a constant

Calculation:

The length of curve of polar coordinates is:

s=βαr2+(drdθ)2dθ

For (drdθ)

drdθ=</

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