   Chapter 10.5, Problem 55E

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 = 1 + sin θ ,       [ 0 , 2 π ]

To determine

To calculate: The length of curve the polar equation r=1+sinθ in the interval [0,2π].

Explanation

Given:

The polar equation is r=1+sinθ and the interval is [0,2π].

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(a)dx=0, d(sinx)dx=cosx and sin2θ+cos2θ=1 here ‘a’ is a constant

Calculation:

The length of curve of polar coordinates is:

s=βαr2+(drdθ)2dθ

For drdθ,

drdθ=ddθ(1+sinθ)drdθ=cosθ

So apply the formula and put for r=1+sinθ, drdθ=cosθ α=2π and β=0

s=02π(1+sinθ)2+(<

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 2340, find the indicated limit. 32. limx2(x2+1)(x24)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In problems 27-30, find. 29.

Mathematical Applications for the Management, Life, and Social Sciences

#### In Exercises 1-22, evaluate the given expression. C(8,6)

Finite Mathematics for the Managerial, Life, and Social Sciences

#### The polar form for the graph at the right is:

Study Guide for Stewart's Multivariable Calculus, 8th

#### True or False: .

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 