Question

Calculate the circulation, \int_c\vec f\cdot d\vec r, in two ways, directly and using stokes' theorem. the vector field \vec f = 5 y\vec i - 5 x\vec j and c is the boundary of s, the part of the surface z = 16 -x^2-y^2 above the xy-plane, oriented upward.

Answer 1

\int_c\vec f\cdot d\vec r, in two ways, directly and using stokes' theorem. the vector field \vec f = 5 y\vec i - 5 x\vec j and c is the boundary of s, the part of the surface z = 16 -x^2-y^2 above the xy-plane, oriented upward.