# Evaluate the line integral

• Jan 17th 2011, 02:12 PM
wopashui
Evaluate the line integral
Show that $F=(\displaystyle \frac{x}{x^2+y^2},\displaystyle \frac{y}{x^2+y^2})$ and $G=(\displaystyle \frac{y}{x^2+y^2},\displaystyle \frac{x}{x^2+y^2})$ are such that one of $F.dP$, $G.dP$ is exact but the other is not.
(dP=(dx,dy)).

Let C be the shorter arc of $x^2+y^2=1$ from $(1/\sqrt{2},-1/\sqrt{2})$ to $(1/\sqrt{2},1/\sqrt{2})$. Evaluate $\int _c\,\!F.dP and \int _c\,\!G.dP$.
• Jan 18th 2011, 08:06 AM
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 $x^2+ y^2= 1$ using the angle a point makes with the x-axis as parameter?
• Jan 18th 2011, 08:38 AM
wopashui
Quote:

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 $x^2+ y^2= 1$ 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