Question

flux integral - see screenshot

Answer 1

the normal vector function of any function is its gradient.

\[F(x,y)=f(x,y)i+g(x,y)j\]\[gradF=n=[\frac{d}{dx}f(x,y)]i+[\frac{d}{dy}f(x,y)]j\]
circle is represented as:
\[F(x,y)=4=x^2i+y^2j\]\[gradF=n=2xi+2yj\]

you an now take the dot product F*n