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Green's Theorem watch

1. Verify Green's theorem in the plane for where C is the closed curve of the region bounded by y = x and y = x^2.

Using Green's theorem I get 13/60. But computing the line integral explicilty I don't get the same answer... I get -1/20.

I'm quite sure 13/60 is the right answer. For the line integral method, I am doing it over C_1, C_2 where:

C_1 : x = t, y = t
C_2 : x = t, y = t^2

And then the line integral = line integral over C_2 - line integral over C_1.

But that dosen't give me 13/60...?!

Any help is appreciated.
2. (Original post by Peter8837)
Verify Green's theorem in the plane for where C is the closed curve of the region bounded by y = x and y = x^2.

Using Green's theorem I get 13/60. But computing the line integral explicilty I don't get the same answer... I get -1/20.

I'm quite sure 13/60 is the right answer. For the line integral method, I am doing it over C_1, C_2 where:

C_1 : x = t, y = t
C_2 : x = t, y = t^2

And then the line integral = line integral over C_2 - line integral over C_1.

But that dosen't give me 13/60...?!

Any help is appreciated.
You have done the area integral wrongly - they should both evaluate to -1/20. Post up some working for the area integral if you want help finding the mistake.
3. (Original post by Farhan.Hanif93)
You have done the area integral wrongly - they should both evaluate to -1/20. Post up some working for the area integral if you want help finding the mistake.
Ahh right I knew one of them was right! Yeah, I've gone through my working and made a mistake which is now fixed. I was fixated on the fact that 13/60 was right that I kept redoing the line integral and kept on getting the same answer (which turned out to be correct!). Thanks for the help.

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