For Comrade Otto Bretscher

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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