1

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: enter image description here

Please tell me if i am in the correct direction, or give me hint how to go about it. Thanks, Anupam

SchrodingersCat
  • 24,472
Anupam Bisht
  • 11

1 Answers1

0

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.

SchrodingersCat
  • 24,472
  • Thank You Sir, Yes, sorry Greens thereom.If I use polar coordiantes then $x^2 +y^2 = r^2 $ but $cos(x) $ will become $cos(rcos(\theta))$ which will complicate the integral.Similarly sin(x) will become $sin(rsin(\theta))$ – Anupam Bisht Nov 08 '15 at 14:33