# Gauss-Kronrod integration Calculator

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

 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
 Generally, this integral can be rapidly and accurately calculated.The integrand f(x) is assumed to be analytic and non-periodic.$\normal Gauss-Kronrod\ integration\\[10](1)\ {\large\int_a^{\hspace{25}b}}f(x)dx={\large\frac{b-a}{2}\int_{\small -1}^{\hspace{25}\small 1}}f({\large\frac{b-a}{2}}y+{\large\frac{b+a}{2}})dy\\(2)\ {\large\int_{\small -1}^{\hspace{25}\small 1}}f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\$

Thank you for your questionnaire.
Sending completion

To improve this 'Gauss-Kronrod integration Calculator', please fill in questionnaire.
Male or Female ?
Male Female
Age
Under 20 years old 20 years old level 30 years old level
40 years old level 50 years old level 60 years old level or over
Occupation
Elementary school/ Junior high-school student
High-school/ University/ Grad student A homemaker An office worker / A public employee
Self-employed people An engineer A teacher / A researcher
A retired people Others
Useful?
Very Useful A little Not at All
Purpose of use?