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!