Vector Line Integral Question I need to compute the line integral for the vector $\vec{F} = \langle x^2,xy\rangle$, for the curve specified: part of circle $x^2+y^2=9$ with $x \le0,y \ge 0$,oriented clockwise.
Once again, I'm stuck at the setup (this happens a lot with me).  I know that I need to parameterize F, but how would I go about doing this exactly?

We have $$F(x,y)=x^2\textbf{i}+xy\textbf{j}$$ and $$C: x^2+y^2=1, x\le0, y\ge0$$ and want to evaluate $$\oint_CF\cdot dr=\int_{\pi}^{\pi/2} F(\cos t,\sin t)\cdot(-\sin t,\cos t)dt=\int_{\pi}^{\pi/2}(\cos^2 t,\sin t\cos t)\cdot(-\sin t,\cos t)dt\\\\\\ =\int_{\pi}^{\pi/2}(-\sin t\cos^2 t+\sin t\cos^2 t)dt=0$$

