Question

The Gauss divergence theorem relates certain (a) surface integrals to volume integrals (b) surface integrals to line integrals (vector quantities to other vector quantities (d) line integráls to volume integrals

Answer 1

The Gauss divergence theorem relates to the conversion of surface integral to volume integrals.

• Gauss divergence theorem: The surface integral of a vector field over a closed surface is equal to the volume integral of the divergence of a vector field A over the volume V enclosed by a closed surface.
• $\int\limits\int\limits\int\limits_{v} \,$ (del.F)dV = $\int\limits\ \int\limits_s {F.n} \, dS$
• Conversion of surface to volume integral or volume to surface integral.
• this theorem is used in solving the double triple integrations.
• Used to find the volume in terms of surface integral using the same function.