# Thread: Evaluate the line integral

1. ## Evaluate the line integral

Show that $\displaystyle F=(\displaystyle \frac{x}{x^2+y^2},\displaystyle \frac{y}{x^2+y^2})$ and $\displaystyle G=(\displaystyle \frac{y}{x^2+y^2},\displaystyle \frac{x}{x^2+y^2})$ are such that one of $\displaystyle F.dP$, $\displaystyle G.dP$ is exact but the other is not.
(dP=(dx,dy)).

Let C be the shorter arc of $\displaystyle x^2+y^2=1$ from $\displaystyle (1/\sqrt{2},-1/\sqrt{2})$ to $\displaystyle (1/\sqrt{2},1/\sqrt{2})$. Evaluate $\displaystyle \int _c\,\!F.dP and \int _c\,\!G.dP$.

2. Okay, what have you done here? What is F.dP? What is G.dP? How you tell if such a "differential" is exact or not?

What is a parameterization for $\displaystyle x^2+ y^2= 1$ using the angle a point makes with the x-axis as parameter?

3. Originally Posted by HallsofIvy
Okay, what have you done here? What is F.dP? What is G.dP? How you tell if such a "differential" is exact or not?

What is a parameterization for $\displaystyle x^2+ y^2= 1$ using the angle a point makes with the x-axis as parameter?
using the angle a point makes with the x-axis as parameter is what i have been struggling to do, I have hard time driving picture of the region