Problem: Find the work done by the force field F(x,y)=<xcos(y), y^2> on a particle that moves along y=x^2 from (-1,1) to (3,9).
So I would be able to do this no problem if it weren't for the y=x^2. That's the part that's messing me up. Normally, you find the equation of the line between the two points, so in this case it would be r(t)=<-1+4t, 1+8t> and then you would find the derivative of that, r'(t)=<4,8> and then find F(r(t))=<(-1+4t)cos(1+8t), (1+8t)^2> then dot the F(r(t)) with r'(t) but what do you do with the y=x^2? I have a feeling it's going to have an effect on r but I can't determine what effect it will have. Cause instead of it having a straight line it's curved so technically finding the equation of the line wouldn't work, correct? So what do I do?! Any help is greatly appreciated!