Use Green’s Theorem to evaluate the integral, assume that the curve C is oriented counterclockwise. Ccos x sin y dx + sin x cosy dy , where C is the triangle vertices (0, 0), (3, 3), and (0, 3).
Added by Charles O.
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Let P(x, y) = cos(x)sin(y) and Q(x, y) = sin(x)cos(y). Then, we have: ∂Q/∂x = cos(x)(-sin(y)) ∂P/∂y = cos(x)cos(y) Now, we can apply Green's Theorem: ∮(P dx + Q dy) = ∬(∂Q/∂x - ∂P/∂y) dA We are given that the curve C is a triangle with vertices (0, 0), (3, 3), Show more…
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