# Gaussian quadrature (Select method) Calculator

## Calculates the integral of the given function f(x) over the interval (a,b) using Gaussian quadrature. (i.e. Gauss-Legendre, Gauss-Chebyshev 1st, Gauss-Chebyshev 2nd, Gauss-Laguerre, Gauss-Hermite, Gauss-Jacobi, Gauss-Lobatto and Gauss-Kronrod)

kinds
1.  Legendre Chebyshev 1st Chebyshev 2nd Laguerre Hermite Jacobi Lobatto Kronrod f(x)
order n
a
1. ,
2. b
α
1. β

 $\normal Gaussian\ quadrature\\\hspace{30} {\large\int_{\small a}^{\hspace{25}\small b}}w(x)f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\\vspace{10}\hspace{20} Quadrature \hspace{30} interval \hspace{10} w(x) \hspace{30} polynomials\\\vspace{5}(1)\ Legendre \hspace{50} [-1,\ 1] \hspace{25} 1 \hspace{90} P_n(x)\\(2)\ Chebyshev\ 1st \hspace{5} (-1,\ 1) \hspace{10} {\large\frac{1}{\sqrt{1-x^2}}} \hspace{70} T_n(x) \\(3)\ Chebyshev\ 2nd \hspace{5} [-1,\ 1] \hspace{10} \sqrt{1-x^2} \hspace{65} U_n(x) \\(4)\ Laguerre \hspace{50} [0,\infty) \hspace{20} x^{\alpha} e^{-x} \hspace{65} L_n^\alpha (x) \\(5)\ Hermite \hspace{50} (-\infty,\infty) \hspace{10} e^{-x^2} \hspace{70} H_n (x) \\(6)\ Jacobi \hspace{75} (-1,\ 1) \hspace{10} (1-x)^{\alpha}(1+x)^{\beta} \hspace{5} J_n^{\alpha,\beta} (x) \\(7)\ Lobatto \hspace{60} [-1,\ 1] \hspace{25} 1 \hspace{80} P_{n-1}^' (x)\\(8)\ Kronrod \hspace{50} [-1,\ 1] \hspace{25} 1 \hspace{90} P_n(x)\\$
 [1-7] /7 Disp-Num5103050100200
[1]  2018/07/16 04:04   Male / Under 20 years old / High-school/ University/ Grad student / Not at All /
Purpose of use
resolução
Comment/Request
faltou as resoluções
[2]  2017/01/21 01:19   Male / 40 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Integrate a tetrahedron
Comment/Request
I wonder if there are differences in results for G-Jacobi quadrature in the function (1+x)^alpha and just x^alpha in terms of getting nodes and weights.
[3]  2015/04/17 07:29   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Study in numerical analysis....
Comment/Request
This Site is very useful
[4]  2015/04/17 07:29   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Study in numerical analysis....
[5]  2015/03/06 18:36   Male / 60 years old level or over / High-school/ University/ Grad student / Very /
Purpose of use
Numerical Analysis Course, implement for exercises
[6]  2014/10/16 23:41   Female / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
study
Comment/Request
very good
[7]  2013/05/28 21:56   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Comment/Request
That will be helpful if the two dimensional (2-D) and 3-D calculations added to the integral calculators.
Best Ragards

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