Line Integral of Clockwise Circle

Question

Considering the circle $x^2+y^2=9$ going in the clockwise direction, I am evaluating the line integral $\int_{C}$ $Fdr$ from $(3,0)$ to $(0,3$). I have parametrization $x=3cost$ and $y=3sint$ and I had a question on the limits of integration, as it is 3/4 of a circle and traveling clockwise. I don't think it is from 0 to $\pi$$/2$ considering the orientation. Any help is appreciated.

Answer 1

Then your limits are $0$ and $-{3\pi \over 2}$ as following$$\int_CF\cdot rd\theta\hat a_\theta=\int_{0}^{-{3\pi \over 2}}3F_\theta(r,\theta) d\theta$$

Answer 2

For clockwise, you want $y = -3\sin(t)$

Answer 3

Alternatively, $$ \int_C F \,\mathrm dr = -\int_{-C} F \, \mathrm dr, $$ where $-C$ is traversed in the anti-clockwise direction.