Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented counterclockwise.The circulation line
integral of F=<(2xy^2),(4x^3)+y> where C is the boundary of {(x,y): 0<=y<=sinx, 0<=x<=pi}
1 answer:
The line integral you need to compute is

By Green's theorem, this is equivalent to the double integral,

where
is the region with boundary
. This integral is equal to

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