Question: reparametrize the curve r(t)=<cos(t)-tcos(t), sin(t)-tsin(t)> : t=0 I know I need to integrate the mag from zero to t but it's not working. got down to the integral of sqrt((t^2)-2t+1) and after a u-sub and a theta sub I got the integral of sec(theta). Then got natural log(sec(theta)+tan(theta)) but if i back sub in I get ln(0) first of all and then a bunch of other nasty problems just i try to solve for t in terms of s. ********* I actually got sqrt((t^2)-2*t+2) the equation for the reparametrization should be s=diffident integral( sqrt((dx/dt)^2)+(dy/dt)^2). I first get sqrt((sin(t)+(t-1)cos(t))^2 + (-sin(t)(1-t)-cos(t))^2) = sqrt(((t^2)-2t+2)(sin(t)^2+cos(t)^2))........ sin(t)^2+cos(t)^2 becomes 1 now i'm left with strictly the integral of sqrt((t^2)-2t+2) evaluated from zero to t I completed the square and got sqrt((t-1)^2 + 1) then u-subbed u=t-1 so integral sqrt(u^2 + 1) i then i used a trig sub to get to just the integral of sec^3(theta) so now i have the integral of sec^3(theta) which equals (1/2)sqrt((t-1)^2 + 1)*(t-1) + (1/2)ln(t + sqrt((t-1)^2 + 1) - 1) and I have to evaluate this from zero to t ...okay and here's my real problem. This question began and a reparametrization so I have to solve for t in terms of s. Other then this being some algebra I haven't worked in a while, I think I can solve it but is there a trig i.d. i missed in the beginning or something? because I don't think a s-parametrization should be this complicated, but maybe i'm wrong.