5. (3 points) Evaluate fe(2x + y)ds, where C is the line segment from (0,2) to...

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5. (3 points) Evaluate fe(2x + y)ds, where C is the line segment from (0,2) to (3,-2), i.e., C : r(t) = (3t, 2 - 4t), 0 ≤ t ≤ 1. 6. (3 points) Let F = (2x³y¹ + 2x, 2x¹y³ +y). Given that f(x, y) = ½¼ x¹y¹ + x² + y² is a potential function of F. Find f Vf. dr, where C is a curve defined by x = t cos(πt) — 1, y = sin(πt/2), 0 ≤ t ≤ 2. 5. (3 points) Evaluate fe(2x + y)ds, where C is the line segment from (0,2) to (3,-2), i.e., C : r(t) = (3t, 2 - 4t), 0 ≤ t ≤ 1. 6. (3 points) Let F = (2x³y¹ + 2x, 2x¹y³ +y). Given that f(x, y) = ½¼ x¹y¹ + x² + y² is a potential function of F. Find f Vf. dr, where C is a curve defined by x = t cos(πt) — 1, y = sin(πt/2), 0 ≤ t ≤ 2.

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5 To evaluate the line integral C 2x y ds along the line segment C from 02 to 32 parameterized by rt ... View the full answer