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I need help with part a of this problem. How do I use Green's theorem to prove the value? (a) Prove that the value of

I need help with part a of this problem. How do I use Green's theorem to prove the value?

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(a) Prove that the value of jig myz alas + (y + 21') dy around any square C only depends on the area of the 0 square and not on its location in R2. Note: no one is claiming that this vector eld is conservative! (b) For R a region bounded by a simple closed smooth curve C, prove that AreaofR2jimdy2yiydm C C (c) Consider the vector eld F : (, ) Let C be any simple closed curve oriented counterclockwise that contains the origin. Prove that % 13" - d7? : 2% in the following way: let Ca be a circle centered at C the origin of radius Oz (counterclockwise) small enough to t entirely within C. Then we can apply Green's theorem the region between Ca and C to prove that

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