Suppose S is the surface x2 y2 z2 1 oriented away from th

Suppose S is the surface x^2 + y^2 + z^2 = 1, oriented away from the origin. Explain why integral integral curl F middot n d sigma is zero for any vector field.

Solution

Let F be a vector field defined on all of R3
. If the component functions of F all have continuous derivatives and curl F = 0, then F is a conservative vector field.