Verify Green's thereom:
$\oint_C (x^2 + y^2 +cos(x))dx +(x^2 +y^2 +sin(y))dy $
where C is the boundary of the semicircle" $${(x,y) \in R^2 :x^2 +y^2 \leq 4,x \geq 0 } $$
Solution:
Please tell me if i am in the correct direction, or give me hint how to go about it. Thanks, Anupam
You have applied the theorem correctly and BTW it is not Stokes' theorem, it should be Green's theorem (on the image/paper).
For R.H.S. you have done the calculations correctly, I haven't checked the answer though and now for the L.H.S. my advice for you is to use polar co-ordinates. The line integral will be as easy as anything.