Evaluate the integral |/ (curl F) •n dA directly for F= [-e", e², e"], S: z = x + y(0 Sx< 1,0

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A: Since, we have to evaluate the line integral given by:-I=∮C xy dx + x2y3  dy -(i)Our aim is to solve…

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A: Line integral

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A: Use Green's Theorem to evaluate the following line integral.

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Q: 3. Compute , xe*ydA where R is the rectangle 0 <x< 1,1< y< 2, using iterated integrals in both…

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A: We will find out the required double integral.

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A: According to Greens theorem :

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Q: Evaluate the line integral by the two following methods. dx + x2 dy Cis counterclockwise around the…

A: The solution is given in the next steps.

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A: Given:Integral ∫02cos (x) dα (x)where α(x) = ∑n=1∞2-nI(x-n-1)

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A: Introduction :

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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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Q: Evaluate the integral, if C is the circular path y = (1-x^2) from (1,0) to (0,1).

A: Let y=1-x2 be circular path from (1,0) to (0,1). Parameterize the above path by taking x=cosθ , then…

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A: Here we have to use green's theorem.

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A: Evaluate the double integral as follows.

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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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A: Given problem:-

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A: First we have to plot region of integration.

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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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Q: Compute the integral | x"dx, with a=1, b=7, and N=5. Answer to three decimals.

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A: From the given integral, Let, 8y^2-y+1 = t ----(1)Now differentiating (1), 16y -1 dy = dt32y -2 dy =…

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A: The vertices of a rectangle 0,0,4,0,4,3 and 0,3. We have to evaluate the integral ∫Cxydx+x2dy.