I've the areas
C1:x2+y2=1
C2:r=2/sqrt(2-cos(θ))
R is the area between C1 and C2, both curves are oriented with positive direction/flow (don't really know the translation of this).
I've found that:
∮ domain of C1 −y/(x2+y2)^2 dx + x/(x2+y2)^2 dy=2π
and
∬ domain(R) 1/(x2+y2)^2 dxdy = π2
How can I use these two results to calculate:
∮ domain of C2 −y/(x2+y2)^2 dx + x/(x2+y2)^2 dy
I'm sure there is a smart way where you subtract 1 result from the other I just can't see it. I know that you have to change the direction of C1 to make this work.
C1:x2+y2=1
C2:r=2/sqrt(2-cos(θ))
R is the area between C1 and C2, both curves are oriented with positive direction/flow (don't really know the translation of this).
I've found that:
∮ domain of C1 −y/(x2+y2)^2 dx + x/(x2+y2)^2 dy=2π
and
∬ domain(R) 1/(x2+y2)^2 dxdy = π2
How can I use these two results to calculate:
∮ domain of C2 −y/(x2+y2)^2 dx + x/(x2+y2)^2 dy
I'm sure there is a smart way where you subtract 1 result from the other I just can't see it. I know that you have to change the direction of C1 to make this work.