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Stoke’s theorem uses the operation of integration—specifically, it relates a surface integral over a surface ( S ) to a line integral over the boundary ( partial S ) of that surface. The mathematical formulation is:
[
iint_S (nabla times mathbf{F}) cdot dmathbf{S} = oint_{partial S} mathbf{F} cdot dmathbf{r}
]
where ( mathbf{F} ) is a vector field, ( nabla times mathbf{F} ) is the curl of ( mathbf{F} ), ( dmathbf{S} ) is a differential area vector on the surface, and ( dmathbf{r} ) is a differential line element along the boundary.
Answer: c
Explanation: ∫A.dl = ∫∫ Curl (A).ds is the expression for Stoke’s theorem. It is clear that the theorem uses curl operation.