# Finding the maximum value of the integral $\int_{C}x^2y-2y^2-5y{dx} +(2xy-y^2x){dy}$

Find the maximum value of $$\int_{C}x^2y-2y^2-5y{dx} +(2xy-y^2x){dy}$$ , where C is closed curve with no self crossing taking in the positive direction.

it is obvious that i need to calculate using green theorem. i got that $$\int_{C}x^2y-2y^2-5y{dx} +(2xy-y^2x){dy}$$ is maximum when the domain is :

D:= $$x^2 + (y-3)^2 \leq 14$$

and i got that this maximum value is :

$$\int_{C}x^2y-2y^2-5y{dx} +(2xy-y^2x){dy}$$ = $$\fbox{\frac{(14)^2\pi}{2}}$$

i am not sure if the answer is right can someone help ?