Surface Integral

For a scalar function over a surface parameterized by and , the surface integral is given by

			(1)
			(2)

where and are tangent vectors and is the cross product.

For a vector function over a surface, the surface integral is given by

			(3)
			(4)
			(5)

where is a dot product and is a unit normal vector. If , then is given explicitly by

(6)

If the surface is surface parameterized using and , then

(7)