# Simpson integration Calculator

## Calculate a table of the integrals of the given function f(x) over the interval (a,b) using Simpson's method.

 The integrand f(x) is assumed to be analytic and non-periodic.It is calculated by increasing the number of partitions to double from 2 to N.$\normal\ Simpson:\\\hspace{20}S={\large\int_a^{\hspace{25}b}}f(x)dx=\hspace{5}{\large\frac{h}{3}}\{f(a)+2{\large \sum_{j=1}^{\frac{n}{2}-1}}f(a+2jh)+4{\large \sum_{j=1}^{\frac{n}{2}}}f(a+(2j-1)h)+f(b)\}\\\hspace{60}h={\large\frac{b-a}{n}}\\$

 f(x) a ,b maximum partition N326412825651210242048 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal \hspace{10}S={\large\int_a^{\hspace{25}b}}f(x)dx\\(1)\ Simpson\\\hspace{20}S_{\normal s}={\large\frac{S_{\normal t}+2S_m}{3}}\\\hspace{45}={\large\frac{h}{3}}\{f(a)+2{\large \sum_{j=1}^{\frac{n}{2}-1}}f(a+2jh)+4{\large \sum_{j=1}^{\frac{n}{2}}}f(a+(2j-1)h)+f(b)\},\hspace{10} h={\large\frac{b-a}{n}}\\$

Simpson integration
 [0-0] / 0 Disp-Num5103050100200
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