matlab program in 3- piont guassian quadrature to evaluate integral f(x)= sin(x/10)

n/a

Answer 1

[Umang Pandey]

Hi @Rikesh,

As per my understanding it appears that you are trying to evaluate the integral of sin(x/10) using Gaussian quadrature 3-point formula.

Here’s how you can do it:

% Define the function 
f = @(x) sin(x/10); 
% Define the integration interval 
a = 0; % Lower limit of integration 
b = pi; % Upper limit of integration 
% Define the 3-point Gaussian quadrature points and weights 
x = [-sqrt(3/5), 0, sqrt(3/5)]; 
w = [5/9, 8/9, 5/9]; 
% Map the Gaussian quadrature points from the interval [-1, 1] to [a, b] 
x_mapped = 0.5 * ((b - a) * x + a + b); 
% Evaluate the function at the mapped Gaussian quadrature points 
f_values = f(x_mapped); 
% Calculate the integral using 3-point Gaussian quadrature 
integral = ((b - a) / 2) * sum(w .* f_values); 
% Display the result 
disp(integral); 

Best,

Umang