According to Simpson’s rule, if there are n number of segments each of width d, in terms of ordinates, area of the figure is:
1
\(A\; = \;\frac{d}{3}\left[ {\left( {{O_1}\; + \;{O_n}} \right)\; + \;4\left( {{O_2}\; + \;{O_4}\; + \; \ldots \; + \;{O_{n - 1}}} \right)\; + \;2\left( {{O_3}\; + \;{O_5}\; + \; \ldots \; + \;{O_{n - 2}}} \right)} \right]\)
2
\(A\; = \;\frac{d}{3}\left[ {\left( {{O_1}\; + \;{O_n}} \right)\; + \;3\left( {{O_2}\; + \;{O_4}\; + \; \ldots \; + \; + \;{O_{n - 1}}} \right)\; + \;2\left( {{O_3}\; + \;{O_5}\; + \; \ldots \; + \;{O_{n - 2}}} \right)} \right]\)
3
\(A\; = \;\frac{d}{3}\left[ {{O_1}\; + \;4\left( {{O_2}\; + \;{O_4}\; + \; \ldots \; + \;{O_{n - 1}}} \right)\; + \;2\left( {{O_3}\; + \;{O_5}\; + \; \ldots \; + \;{O_n}} \right)} \right]\)
4
\(A\; = \;\frac{d}{3}\left[ {{O_1}\; + \;2\left( {{O_2}\; + \;{O_4}\; + \; \ldots \; + \;{O_{n - 1}}} \right)\; + \;3\left( {{O_3}\; + \;{O_5}\; + \; \ldots \; + \;{O_n}} \right)} \right]\)