- The line integral along the curve C can be written as
- where C is parametrisized as r(t) with the parmeter t.
∫¦r'(t)¦ dt equals the arc length i.e. the length of the curve.
Consider eg the circle. x2+ y2 = r2. This can be parametrisized as follows
x(t) = cos(t)
y(t) = sin(t)
The perimeter of the circle can then be calculated according to
∫ sint2+cos2t dt= 2π