Question: Evaluate the line integral by two methods: (a) Directly (b) Using Green's Theorem. C is the rectangle with vertices (0, 0), (3, 0), (3, 1),

Evaluate the line integral by two methods:

(a) Directly

(b) Using Green's Theorem.

C is the rectangle with vertices (0, 0), (3, 0), (3, 1), and (0, 1)

Data from Green's Theorem

Let C be a positively oriented, piecewise-smooth, simple closed curve in the plane and let D be the region bounded by C. If P and Q have continuous partial derivatives on an open region that contains D, then

If | Pdx + Q dy = D dA

Data from Green's Theorem

If | Pdx + Q dy = D dA

foxy dx + x dy,

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