Problem: Evaluate Integral F dot dr, where C is the boundary of the region R and C is oriented so that the region is on the left when the boundary is traversed in the direction of its orientation.(adsbygoogle = window.adsbygoogle || []).push({});

F(x,y)=(e^(-x)+3y)i+(x)j

C is the boundary of the region R inside the circle x^2+y^2=16 and outside the circle x^2-2x+y^2=3

2. Relevant equations

Integral F dot dr=DOuble integral over the region R, (dg/dx-df/dy)dA

3. The attempt at a solution

I started by completing the square of that circle that is not centered at the origin, and got (x-1)^2+y^2=4. So now I know the inner region's boundary is a circle of radius 2 centered at (1,0).

Also, I got the double integral over x^2+y^2=16 , Double integral 0to 2pi, 0 to 4 (-2)r dr dtheta and got -32pi.

But I don't know what to do from here. The circle x^2-2x+y^2=3 is giving me a hard time. Can you tell me how to do the rest of this problem?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Green's Theorem with a circle not centered at the origin.

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**