## Calculates the integral of the given function f(x) over the interval (a,b) using Gauss-Kronrod quadrature.

 The integration value is calculated in the following procedures.(1) Calculates using Gauss-Legendre rule at order (n-1)/2.(2) Calculates using Gauss-Kronrod rule at order n.(3) Indicates the accuracy between (1) and (2).$\normal{\large\int_{\small -1}^{\hspace{25}\small 1}}f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\$

 f(x) a b order n3579111315171921232527293133353739414345474951535557596163656769717375777981838587899193959799of Kronrod, n=3,5,7,..   (odd) 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 The integrand f(x) is assumed to be analytic and non-periodic.$\normal Gauss-Kronrod\ integration\\[10](1)\ {\large\int_a^{\hspace{25}b}}f(x)dx={\large\frac{b-a}{2}\int_{\small -1}^{\hspace{25}\small 1}}f({\large\frac{b-a}{2}}y+{\large\frac{b+a}{2}})dy\\(2)\ {\large\int_{\small -1}^{\hspace{25}\small 1}}f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\$

 [1-2] /2 Disp-Num5103050100200
[1]  2014/03/19 07:22   Male / 40 years old level / A teacher / A researcher / A little /
Purpose of use
I am trying to replicate the numerical integration technique used in a Texas Instrument TI-84 i.e. fnInt().
[2]  2013/07/13 00:45   Male / 20 years old level / A teacher / A researcher / A little /
Purpose of use
Testing
Comment/Request
Can you please allow these calculators to show all of the intermediate calculations? That would be an immense help and I typically will not use these (although they are wonderfully done) because I cannot see those results. Thanks

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