- #1
mottov2
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Homework Statement
Find the parameterized curve gamma and vector field F so that
the [itex]\int[/itex][itex]\gamma[/itex] F ds = [itex]\int[/itex][itex]\int2xy dx dy[/itex] by Green's Theorem.
where -2<y<2
1-sqrt(4-y2) < x < 1+sqrt(4-y2)
The Attempt at a Solution
x = 1 + sqrt(4-y2)(x-1)2=4-y2
(x-1)2+y2=4
so the path is a circle centered at (1,0) with radius of 2.
parametrize this by setting x = 1+2Cos(t) and y = 2Sin(t)
for the vector field I got F = (xy2,2x2y)
but is there more than one possible vector field?