Quiz 3 11 6 14 Math 2E Discussion Prof Laure Giovangigli Name Instructions Show all your work and simplify your answers completely No calculators notes books etc may be used during the quiz 1 Compute the line integral Student ID Number cid 90 Solution 1 Written in the form cid 82 where C is x2 y2 1 C 2xe ydx 2y x2e y dy C P dx Qdy we have P 2xe y Q 2y x2e y Then we have Hence Therefore integrating a conservative vector eld over a closed curve yields the value to be 0 2 Compute the line integral where C is the circle x2 y2 1 Solution 2 We have P y3 and Q x3 Then 3x2 and so by Green s Theorem we have cid 90 C P dx Qdy 2xe y 2xe y Q x P y Q x P y 0 y3dx x3dy cid 90 C Q x P y 3y2 cid 90 cid 90 3 3 D Q x cid 90 cid 90 cid 90 2 D 0 cid 90 1 cid 32 0 1 4 3 2 3 2 P y dA x2 y2dA r2rdrd cid 33 cid 12 cid 12 cid 12 cid 12 r 1 r 0 r4
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