Let $F(x,y)=(x,y)$. Let $C$ be the portion of the ellipse $(x^2/a^2)+(y^2/b^2)=1$ in quadrants 1 and 2. Show how to evaluate $\int_C F \cdot dr.$
this is the question i am given. i am not sure if what i am doing is right but this is what i have.
$$x=a \cos t \ \ \ \implies \ \ \ dx/dt=-a \sin t $$
$$y=b \sin t \ \ \ \implies \ \ \ dy/dt = b \cos t$$
(integral along the curve)xdx+(integral along the curve)ydy