# Trapezoid, Midpoint and Simpson integration Calculator

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

 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.
 f(x) a , b maximum partition N 32 64 128 256 512 1024 2048 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal \hspace{40}S={\large\int_a^{\hspace{25}b}}f(x)dx\\(1)\ Trapezoid\hspace{5}S_{\normal t}={\large\frac{b-a}{2}}\{f(a)+f(b)\}\\(2)\ Midpoint\hspace{10}S_m=(b-a)f({\large\frac{a+b}{2}})\\(3)\ Simpson\hspace{10}S_{\normal s}={\large\frac{S_{\normal t}+2S_m}{3}}\\\hspace{105}={\large\frac{b-a}{6}}$f(a)+4f({\large\frac{a+b}{2}})+f(b)$\\$
Trapezoid, Midpoint and Simpson integration
 [1-9] /9 Disp-Num5103050100200
[1]  2018/11/14 11:24   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
Figuring out percent error
[2]  2018/07/28 20:24   Female / 20 years old level / High-school/ University/ Grad student / A little /
Purpose of use
to calculate fast the rules
[3]  2018/01/29 22:34   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
homework help
Comment/Request
let me be able to choose the n value
[4]  2017/11/02 05:58   - / 40 years old level / High-school/ University/ Grad student / Very /
Purpose of use
homework
Comment/Request
it helps a lot
[5]  2017/03/14 15:58   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
[6]  2017/01/18 00:49   Male / 20 years old level / High-school/ University/ Grad student / A little /
Comment/Request
why not summarise all result in a file, which is more practical for usage
[7]  2012/11/23 23:19   Female / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
for doing mathlab calculation
Comment/Request
how can i get the tolerance and please the law to get tolerance
[8]  2009/11/06 21:52   - / - / - / Very /
Comment/Request
(b-a)/6 should be (b-a)/3 in simpson
[9]  2009/03/20 01:06   Male / 20 level / A researcher / Very /
Comment/Request
Its Amazing.

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