Curvilinear Integral / Surface Integral
Curvilinear integral
is the equation of a curve
that connects two points 
, where 
is the arc lengthFor points
, assume that 
Points
are considered on 
is the length of curve 
denotes a random point on curve 
The curvilinear integral is calculated along curve
in the scalar field 
and 
If
is a closed curve, we have
The curvilinear integral is calculated along curve
in the vector field 
Surface integral
is the surface bounded by a closed curve 
Supposed that
is partitioned into small parts with areas 
is a random point on 
The surface integral is calculated on surface
in the scalar field 
It can also be expressed as
If the surface
satisfies 
, then
The surface integral is calculated on surface
in the vector field 
[0]Top