1. The problem statement, all variables and given/known data Evaluate the line integral [tex]\[ \int_c yz\,ds.\][/tex] where C is a parabola with z=y^2 , x=1 for 0<=y<=2 2. Relevant equations A hint was given by the teacher to substitute p=t^2 , dp=(2t)dt and use integration by parts. I also know from other line integrals with respect to arc length that: ds=sqrt((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2) 3. The attempt at a solution I think that from the information given, the beginning and end points are (1,0,0) to (1,2,4). My first guess is: x(t) = t y(t) = 2t z(t) = t^2 This will be when t goes from 0 to 2. So after I have parameterized the curve, I would substitute the functions of t back into the integral to get: int((2t)^3*sqrt(1^2+2^2+(2t)^2),t,0,2) =8*int(t^3*sqrt(4t^2+5),t,0,2) =12032/3 This doesn't look right to me though. Any help would be appreciated!