Stokes’ theorem can be generalized to piecewise smooth surfaces, like the union of sides of a polyhedron. Here, we take the integral over the sides as the sum of integrals over each individual side.
Would anyone please help me to understand the sentences. Stokes' theorem
$$\int_C f \cdot dr = \int\int_S (\nabla \times f) \cdot n\, dS. $$ Second sentence: "Here, we take the integral over the sides as the sum of integrals over each individual side." what does it mean... Is it "Here, we take the surface integral over the sides as the sum of surface integrals over each individual side."...does it mean surface integral as $\int\int_{S} (\nabla \times f) \cdot n\, dS= \sum_i\int\int_{S_i} (\nabla \times f) \cdot n\, dS $