I'm not sure what I got wrong. I came out with the integral
(3sqrt(2)/2),(0) (sqrt(9-y^2)^2), (y) 4-2 dy dx
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Well it looks like you did two things wrong. The first and most important is that ∂F_1/∂y = -2, so you should have had 4-(-2) =6, not 4-2=2. The second might be that your integral should have been dxdy not dydx. Also, a) the integrand is a constant and so polar integration might be easier, and b) the area of a pie wedge is (1/2)(Δθ)r^2, which is to say (9π/8) you could use that instead of doing an integral
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