Let S be the sphere x^(2)+y^(2)+z^(2)=1 and F_(x,y,z)=(5x^(3),5y^(3),xy). State the Gauss's Theorem. Use this Theorem to find the outward flux of F_() through the surface of S.


A) Gauss's Theorem states that the flux of a vector field through a closed surface is equal to the divergence of the vector field integrated over the volume enclosed by the surface.
B) Gauss's Theorem states that the flux of a vector field through a closed surface is equal to the curl of the vector field integrated over the volume enclosed by the surface.
C) Gauss's Theorem states that the flux of a vector field through a closed surface is equal to the line integral of the vector field along the boundary of the surface.
D) Gauss's Theorem states that the flux of a vector field through a closed surface is equal to the gradient of the vector field integrated over the volume enclosed by the surface.