Curl, or circulation, Flux or divergence both can be expressed in Green’s theorem cleverly and clearly explained by Dr. Trefor Bazett.

Moving up to a higher lever – cubic -using an example of a cone, to describe it with parameterization format, and then try to compute it’s surface area.

There is this critical crux – been proved in linear algegra or other parts in math that the cross product, which is a vector has the ‘direction’ perpendicular to both component vectors and the ‘value’ equal to the area formed by the two component vectors, hence

Then calculate surface of a sphere:

Third example: