1. The problem statement, all variables and given/known data Explain why ∫(1+(1/x2)1/2dx over [1,e] = ∫(1+e2x)1/2dx over [0,1] 3. The attempt at a solution The two original functions are ln(x) and ex and are both symmetrical about the line y = x. If I take either of the functions and translate it over the line y = x the two functions will match up completely. So it seems reasonable that the arc lengths will be the same over some region. If I plug in the bounds 1 and e into ln(x) i get 0, and 1 and if I plug the bounds 0,1 into ex I get 1, and e. I don't really know how it helps but it's something I suppose.