Right choice is (a) Mean value theorem
Easy explanation: The Green-Gauss theorem states that for a closed volume V with the surrounding surface ∂V and outward pointing incremental surface vector d(vec{S}),
∫V (
ablaPhi dV=∮_{∂V} Phi dvec{S})
Using the mean value theorem,
∫V ∇ΦdV=(overline{
ablaPhi} V)
Where, (overline{
ablaPhi} V) is the average gradient over the volume V.
