## 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 n 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 of Kronrod,  n=3,5,7,..   (odd)
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 The integrand f(x) is assumed to be analytic and non-periodic.$\normal Gauss-Kronrod\ integration\\[10](1)\ {\large\int_a^{\hspace{25}b}}f(x)dx={\large\frac{b-a}{2}\int_{\small -1}^{\hspace{25}\small 1}}f({\large\frac{b-a}{2}}y+{\large\frac{b+a}{2}})dy\\(2)\ {\large\int_{\small -1}^{\hspace{25}\small 1}}f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\$

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