   Chapter 10.5, Problem 53E

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 = 4 sin θ ,       [ 0 , π ]

To determine

To calculate: The length of curve the polar equation r=4sinθ in the interval [0,π].

Explanation

Given:

The polar equation is r=4sinθ and the interval is [0,π].

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(sinx)dx=cosx, sin2θ+cos2θ=1 And (a)dx=ax here ‘a’ is a constant

Calculation:

The length of curve of polar coordinates is:

s=βαr2+(drdθ)2

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