## Calculates the integral of the given function f(x) over the interval (a,b) using Gauss-Chebyshev 2nd quadrature.

 $\normal Gauss-Chebyshev\ 2nd\ quadrature\\[10]{\large\int_{\small -1}^{\hspace{25}\small 1}}\sqrt{1-x^2}f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\ {\large\int_a^{\hspace{25}b}}g(x)dx\simeq{\large\frac{b-a}{2}\sum_{\small i=1}^{n}}{\large\frac{w_i}{\sqrt{1-x_i^2}}}g({\large\frac{b-a}{2}}x_i+{\large\frac{b+a}{2}})\\\vspace{20}$

 g(x)f(x) interval (a ,b) partition n23456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 The integrand f(x) is assumed to be analytic and non-periodic.$\normal Gaussian\ quadrature\\\hspace{10} {\large\int_{\small a}^{\hspace{25}\small b}}w(x)f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i), \ {\large\int_{\small a}^{\hspace{25}\small b}}g(x)dx\simeq{\large\sum_{\small i=1}^{n}}{\large\frac{w_{i}}{w(x_i)}}g(x_i)\\Gauss-Chebyshev\ 2nd\ quadrature\\\hspace{30} interval(a,b):\hspace{20} [-1,\ 1]\\\hspace{30} w(x):\hspace{80} \sqrt{1-x^2}\\\hspace{30} polynomialsl:\hspace{10} U_n (x)\\$

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