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

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

 f(x) a ,b partition n23456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100n=2,3,4,..,100 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 The integrand f(x) is assumed to be analytic and non-periodic.$\normal Gaussian\ quadrature\\\hspace{20} {\large\int_{\small a}^{\hspace{25}\small b}}w(x)f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\Gauss-Lobatto\ quadrature\\\hspace{30} interval(a,b):\hspace{20} [-1,\ 1]\\\hspace{30} w(x):\hspace{80} 1\\\hspace{30} polynomials:\hspace{10} P'_{n-1} (x)\\$

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