- #1
SapphireLFC
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Homework Statement
Solve: ∫(-ydx+xdy)/(x2+y2) counterclockwise around x2+y2=4
Homework Equations
Greens Theorem:
∫Pdx + Qdy = ∫∫(dQ/dx - dP/dy)dxdy
The Attempt at a Solution
Using Greens Theorem variables, I get that:
P = -y/(x2+y2) and
Q=x/(x2+y2)
and thus dQ/dx = (y2-x2)/(y2+x2)2
and dP/dx = (y2-x2)/(y2+x2)2
So, ∫∫(dQ/dx - dP/dy)dxdy = ∫∫( (y2-x2)/(y2+x2)2 - (y2-x2)/(y2+x2)2)dxdy
... which means I'm integrating 0 (which can't be right as that would equal 0 over a definite integral). Not sure where I've gone wrong! Can anyone spot an error?