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5. (1 Point) Problem 5 (Evaluated for justification and written explanation) Suppose you agree to tutor your friend in M273 before the final exam. They
5. (1 Point) Problem 5 (Evaluated for justification and written explanation) Suppose you agree to tutor your friend in M273 before the final exam. They are heavily struggling with Green's Theorem, so you sit down to help them revise their homework solutions. The first problem you decide to work through is this one: A particle starts at the point (2, 0), moves along the r-aris to the point (-2, 0), then along the semicircle y = v4 -x2 to the starting point. Use Green's Theorem to find the work done on this particle by the force field F(x, y) = (x, 23 + 3xy?). Your friend's solution to this problem was: Using Green's Theorem, we will convert this to a double integral. Let D denote the inside of the semi-circular path that the particle traverses. The integrand of this double integral will be a ay [a3 + 3ry?] = 1 -6ry So, we must evaluate the integral 1 1-GaydA = [ 1-baydy da L (2-121) do = (2x - 627) =4-24 = -20 Your friend's solution has three major issues - one with the integrand, one with the setup of the double integral, and one with the general use of the theorem. Identify all three of these issues, and explain (specifically) how you would fix them. Explanation: (Use complete sentences)
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