Question

Using Green's Theorem evaluate the integral ∮c(xydx + x^2y^2 dy) where C is the triangle with vertices (0 ,0), (1, 0) and (1, 2).

Answer 1

well, you have

M = xy
N = x^2y^2

so the integral is just

∫∫_R (N_x - M_y) dx dy

Along y=0, dy=0,
Along x=1, dx=0,
Along y=2x, dy = 2dx

Now just break the boundary into three parts, and evaluate each part. Watch the direction of the limits.

Answer 2

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