I must evaluate $\displaystyle I=\int_C F dr$ where $\displaystyle C$ is described by $\displaystyle r(t)=(t^2,t^3)$, $\displaystyle 0\leq t\leq 1$. $\displaystyle F(x,y)=(e^x,xy)$.

My attempt : $\displaystyle |r'(t)|=\sqrt{4t^2+9t^4}$.

$\displaystyle I=\int_0^1 (e^{t^{2}}+t^5)\sqrt{4t^2+9t^4}dt$. I don't think I've made it right... Seems hard to solve.