Evaluate the line integral by the two following methods. $(x- y) dx + (x + y) dy C is counterclockwise around the circle with center the origin and radius 5 (a) directly (b) using Green's Theorem

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A: A detailed solution is given below.

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A: Given problem:-

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 5…

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A: To evaluate: ∮C5y2dx+5x2dy Let, L=5y2& M=5x2⇒∂L∂y=10y, ∂M∂x=10x

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A: According to Greens theorem :

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A: Green's Theorem, ∫CPdx+Qdy=∬D∂Q∂x-∂P∂ydA Compare ∫CPdx+Qdy=∫Cyexdx+2exdy Implies that, P=yex, Q =…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p…

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Q: Evaluate the line integral by the two following methods. dx + x?y3 dy C is counterclockwise around…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly.…

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A: using cauchy residue theorem to find given integral...

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A: I solved it using both method

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Q: evaluate the iterated integral.

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 5…

A: We have to evaluate the line integral using Green's theorem and check the answer by evaluating it…

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Q: Use Green's Theorem to evaluate the following line integral. Of dy -g dx, where (f.g) = (7x²,8y?)…

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