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Let's now attempt to apply Stokes' theorem

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And so over here we have this little diagram, and we have this path

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that we're calling C, and it's the intersection of the plain Y+Z=2, so that's the plain that

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kind of slants down like that, its the intersection of that plain

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and the cylinder, you know I shouldn't even call it a cylinder

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because if you just have x^2 plus y^2 is equal to one, it would essentially be like a pole,

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an infinite pole that keeps going up forever and keeps going down forever

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so it would never have a top or a bottom

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but we slice that pole, with y plus z is equal to 2, to get where they intersect

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we get our path C. We also have this vector field defined in this way