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1. (a) Determine whether or not F is a conservative vector field. If it is, find...

1. (a) Determine whether or not F is a conservative vector field. If it is, find the potential function for F.

(b) Evaluate R C1 F · dr and R C2 F · dr where C1 is the straight line path from (0, −1) to (3, 0), while C2 is the union of two straight line paths: first piece from (0, −1) to (0, 0) and then second piece from (0, 0) to (3, 0). (When applicable, use the Fundamental Theorem of Line Integrals!!)

F(x, y) = (xy + y 2 )i + (x 2 + 2xy)j.

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