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categoryرياضيات schoolبكالوريوس event_available2026-07-15

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12. (2+4+4+3 pts) Suppose that F(x, y) = (x, y+1) and C is the upper semicircle that starts at (-2,0) and ends at (2,0). (a) Sketch and parameterize the curve C. (b) Show F is a conservative vector field. (c) Find a function:= f(x, y) such that Vf-F. (d) Evaluate LF F-dr using the fundamental theorem for line integrals.

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