# Line Integral of Clockwise Circle

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.

## 3 Answers

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

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

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