Area Using Parametric Equations
Parametric Integral Formula
The area between the x-axis and the graph of x = x(t), y = y(t) and the x-axis is given by the definite integral below. This formula gives a positive result for a graph above the x-axis, and a negative result for a graph below the x-axis.
Note: If the graph of x = x(t), y = y(t) is partly above and partly below the x-axis, 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 x-axis and the first period of the cycloid |
See also
Parametrize, parametric equations, area under a curve, area using polar coordinates
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