Evaluate the line integral $\displaystyle \int^._c F \cdot dr $

where C is the portion of the parabola y = x^2 from (0,0) to (1,1) if $\displaystyle F(x,y) = <3ye^{xy}, 3x^2> $

This is what i get. Can anyone check this for me please thanks!

$\displaystyle c: r(t) = <t,t^2> $ where 0<t<1

$\displaystyle \frac{dr}{dt} = <1,2t> $

$\displaystyle F(r(t)) = <3te^t^3, 3t^2> $

$\displaystyle F(r(t)) \cdot \frac{dr}{dt} = <3t^2e^t^3, 3t^2> \cdot <1,2t> = 3t^2e^t^3 + 6t^3 $

$\displaystyle \int_0^1 3t^2e^t^3dt + \int_0^1 6t^3dt$

$\displaystyle (e-1) + \frac{3}{2} = e + \frac{1}{2} $

Thanks for looking over this