(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I was wondering if I did this problem correctly as I don't have the solution, also wanted to make sure that my limits of integration were correct as they tend to be tricky in finding arc length in polar coordinates.

x(t)=arcsint

y(t)=ln(sqrt(1-t^2))

2. Relevant equations

S= integral from a-b of

sqrt((dx/dt)^2+(dy/dt)^2)dt

3. The attempt at a solution

(dx/dt)^2=1/(1-t^2)

(dy/dt)^2=t^2/(1-t^2)^2

adding (dx/dt)^2+(dy/dt)^2

I get 1/(1-t^2)^2

Put all of this into the square root as said by the formula

I simplified it to the integral from 0 to 1/2 of dt/(1-t^2)

Factoring the bottom I get dt/((1-t)(1+t))

by Partial Fractions I get

2 separate integrals

(1/2)∫dt/(1-t)+(1/2)∫dt/(1+t)

Finally integrating this I get

(1/2)(ln(1-t)+ln(1+t))

Plugging in my limits of integration I get

(1/2)(ln(1/2)+ln(3/2))

Using the log rule

I get ln(3/4)^(1/2)

Thank you so much to anyone who read through this long problem!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Find the arc length of the curve (Polar)

**Physics Forums | Science Articles, Homework Help, Discussion**