## 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 n 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 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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