Area Using Parametric
Equations
Parametric Integral Formula
The area between the xaxis
and the graph of x = x(t), y = y(t)
and the xaxis is given by the definite
integral below. This formula gives
a positive result
for a graph above the xaxis,
and a negative result
for a graph below the xaxis.
Note:
If the graph of x = x(t), y = y(t) is partly above and partly below the xaxis, the
formula given below generates the net area. That is, the
area above the axis minus the area
below the axis.
Formula: 

Example: 
Find the area of the between the xaxis
and the first period of the cycloid x = t – sin
t, y = 1 – cos
t. The values of t run from 0 to 2π.

See
also
Parametrize, parametric
equations,
area under a curve, area
using polar coordinates
