The correct answer is: A. a line integral and a surface integral.
Stokes’ theorem states that the integral of the curl of a vector field over a surface is equal to the line integral of the vector field around the boundary of the surface. In other words, it relates the circulation of a vector field around a closed curve to the flux of the curl of the vector field through a surface bounded by the curve.
The curl of a vector field is a measure of how much the vector field is rotating. The flux of a vector field through a surface is a measure of how much the vector field is crossing the surface.
Stokes’ theorem can be used to calculate the circulation of a vector field around a closed curve if the flux of the curl of the vector field through a surface bounded by the curve is known. It can also be used to calculate the flux of a vector field through a surface if the circulation of the vector field around the boundary of the surface is known.
Option B is incorrect because Stokes’ theorem does not connect a surface integral and a volume integral. Option C is incorrect because Stokes’ theorem does not connect a line integral and a volume integral. Option D is incorrect because Stokes’ theorem does not connect the gradient of a function and its surface integral.