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

 $\normal Gauss-Legendre\ quadrature\\[10]{\large\int_{\small -1}^{\hspace{25}\small 1}}f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\{\large\int_a^{\hspace{25}b}}f(x)dx\simeq{\large\frac{b-a}{2}\sum_{\small i=1}^{n}}w_{i}f({\large\frac{b-a}{2}}x_i+{\large\frac{b+a}{2}})\\\vspace{20}$
 f(x) a , b partition 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.$\normal Gaussian\ quadrature\\\hspace{20} {\large\int_{\small a}^{\hspace{25}\small b}}w(x)f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\Gauss-Legendre\ quadrature\\\hspace{30} interval(a,b):\hspace{20} [-1,\ 1]\\\hspace{30} w(x):\hspace{80} 1\\\hspace{30} polynomialsl:\hspace{10} P_n (x)\\$
 [1-7] /7 Disp-Num5103050100200
[1]  2017/11/02 17:07   Male / 20 years old level / High-school/ University/ Grad student / Useful /
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Need to check answer for assignment.
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Thanks..
[2]  2017/10/25 09:47   Female / 20 years old level / High-school/ University/ Grad student / Very /
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Numerical Analysis II
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Thanks!! very good and accurate
[3]  2016/03/23 00:09   Female / 20 years old level / High-school/ University/ Grad student / Useful /
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check homework
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needs instructions on how to properly enter inverse trigonomic functions.
[4]  2012/02/17 17:29   Male / 20 years old level / A student / Very /
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LECTURE ASSIGNMENTS
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IMPORTANT
[5]  2010/06/22 21:49   Male / More than 60 / Others / Very /
Purpose of use
High precision integration calculations
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A wonderful resource. Thank you.
[6]  2010/06/05 08:36   Male / More than 60 / Others / Very /
Purpose of use
High precision Gauss-Legendre integration
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A truly magnificent resource.Thank you!! A suggestion. I've just calculated a 50 digit integral result, and I wish to divide it by another number. How do I do that? I cannot find the option to handle high precision numbers and the basic functions, like +. -. etc. Is there a way? Thanks again for a powerful tool.
[7]  2010/06/05 08:26   Male / More than 60 / Others / Very /
Purpose of use
High precision Gauss-Legendre integration
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A truly magnificent resource.Thank you!!

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