How do you convert divergent to surface integral? - Answers

To convert a divergence to a surface integral, you can use the Divergence Theorem, which states that for a vector field (\mathbf{F}) defined in a region (V) with a smooth boundary surface (S), the integral of the divergence of (\mathbf{F}) over (V) is equal to the flux of (\mathbf{F}) across (S). Mathematically, this is expressed as: [ \int_V (\nabla \cdot \mathbf{F}) , dV = \iint_S \mathbf{F} \cdot \mathbf{n} , dS ] where (\mathbf{n}) is the outward unit normal to the surface (S). Thus, you can transform a volume integral of divergence into a surface integral by applying this theorem.