Use a line integral on the boundary to find the area


I'm little confused to use green's theorem for the area with using C1 and C2 curves. I tried to find the area by using polar coordinates but I ended up with a diverging integral. I calculated the line integrals for each curve and added them up and got ${\pi}/4-3/2$ which is negative.

I basically used$\int ydx$ on C1 and C2 Can anyone help me how I can solve this?

edit: I used $ 1/2\int xdy-ydx$ for C1 and C2 and got ${\pi}/4-1/2$ which I suppose it's the right answer.


  • $\begingroup$ I think there is some calculation mistake made...the area should be $\pi/4-1/2$, without even using integration. $\endgroup$ – Brian Cheung Nov 27 '16 at 10:22

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