These two problems are dealing with finding the length of a curve, I just have some problems determining what ds is before I set up the integral. I just need to know if I'm heading in the right direction....
1. x= cos t; so dx= -sin t...y= t+sin t; so dy= 1+cos t. I then plug these values for dx and dy into the formula for ds, squrt[(-sin t)^2+(1+cos t)^2] dt...I then get this to boil down to squrt(2+2 cos t) dt. This is where I've hit the wall. Does this even need a u sub to set up the integral?
2. x=(t^2)/2; so dx= t...y=[(2t+1)^3/2]/3; so dy=[(2t+1)^1/2]/2. I then plug these values into the formula for ds, squrt[(t)^2+(2t+1)^1/2)/2)^2 dt. I get this simplified to squrt(t^2+1/2t+1/4) dt. I'm stumped at this point here too. I don't see how a u sub would help setting up the integral.
Thanks to anyone who takes the time to look this over....
~CC