The electric potential V(x) in a region around the origin is given by $V\left(x\right) = 4x^2$ volts. The electric charge enclosed in a cube of 1 m side with its centre at the origin is (in coulomb)

$$\begin{gathered} \overrightarrow{E}=-\frac{dv}{dx}=-8x. \\ As the centre of the cube is at origin, \\ Net flux = \oint \overrightarrow{E}.d\overrightarrow{A} =\int \overrightarrow{E_x}.\overrightarrow{A} \\ Net outward flux=\left(flux through surface at x=-\frac{1}{2}\right)+\left(flux through surface at x=+\frac{1}{2}\right) \\ Total flux = \left(\left(-8x\frac{-1}{2}\right)\hat{i}.\left(-\hat{i}\right)\right)+\left(\left(-8x\frac{1}{2}\right)\hat{i}.\hat{i}\right)=-8 \\ Total flux=\frac{Q_{enclosed}}{{\epsilon }_o} \\ \Rightarrow Q_{enclosed}=-8{\epsilon }_o \end{gathered}$$