Trapezium Rule

The trapezium rule is a method used in calculus to calculate the area under a curve. In calculus language, the area under a curve is the integral of the function defined by the curve.

The integral is given by:

                     Considering the figure below, it implies that the above expression can be used to get a summation of the individual are components bound by the curve. If equal widths are used, then x2-x1=Ts.

The new expression then becomes 

However, Simpson's rule is more accurate when the curve is parabolic.