Calculus Level 5

Evaluate the flux integral , $$\int \int_{S}\vec{G}.d\vec{S}$$ where $$S$$ is the part of the surface $$z=8-x^{2}-y$$ inside the cylinder , $$x^{2}+y^{2}=1$$ oriented with normals pointing upward, and $$\vec{G}$$ is the vector field , $$\vec{G}(x,y,z)=\left \langle 0,2z,2y-2y^{2} \right \rangle$$

The answer is of the form $$A\pi$$ submit the value of $$A$$

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