This is right. You just made a little mistake in the first component of F(r(t)). It has a factor of t^2 (not t). You actually corrected this later on, so your answer is correct.
Also, it should be dr/dt (not just dr).
Evaluate the line integral
where C is the portion of the parabola y = x^2 from (0,0) to (1,1) if
This is what i get. Can anyone check this for me please thanks!
where 0 < t < 1
Thanks for looking over this