## Demonstration

Is $F(x,y,z) = P(x,y,z)i+Q(x,y,z)j+R(x,y,z)k$ a vector field which has second-order partial derivatives continuous at all points an open that contains a surface oriented, with normal N and whose board is a regular curve c. Demonstrate that:

$\int_c F.dr = \int \int_S (curl(curlF)).N.ds$