1. The problem statement, all variables and given/known data Given y = 156 - (x - 40)2/60. x = 0 and x = 85 Find distance traveled 2. Relevant equations Arc Length S = integral of square root of ( y' )2 3. The attempt at a solution Doing this I get the trig sub tan(t) = (x - 40)/ 30 (Told by teacher to use this instead of -(x - 40)/30 ) so x = 30tan(t) + 40 and dx = 30sec2(t) So then under the radical I get 1 + ( - (tan (t) )2 So is this equal to the square root of sec2(t)? Assuming it is, I get the integral of sec2(t) times 30sec2(t) or sec3(t) I know how to do this (I think) but I'm really not sure (I can't use what's written in the back of my book). Doing the work I get: S(x) = 15sec(t)tan(t) + (1/2) ln[ (sec(t) + tan(t) ] Substitution x back in for t gives tan(t) = (x-40)/30 and sec(t) = square root [ 1 + ( ( -x + 40)/(30) )2 But evaluating this from 0 to 85 gives me an arc length of ~ 75.05, which I know can't be right, but I can't figure out where I went wrong.