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

n/a

[Mahesh]

Consider the following integral: R 3 0 xe2x dx Write all the relevant commands on a MATLAB script to compute the value of the above integral using two-point Gaussian quadrature rule

Answer 1

[Avni Agrawal]

Hi Rikesh,

I understand that you are trying to evaluate the integral of using the 3-point Gaussian quadrature method.

Here is step by step explanation on how to do this:

1. Define the Function and Interval:

f = @(x) sin(x/10);
a = 0; % Lower limit
b = pi; % Upper limit

2. Gaussian Quadrature Points and Weights:

x = [-sqrt(3/5), 0, sqrt(3/5)];
w = [5/9, 8/9, 5/9];

3. Map Points and Evaluate Function:

x_mapped = 0.5 * ((b - a) * x + a + b);
f_values = f(x_mapped);

4. Compute the Integral:

integral = ((b - a) / 2) * sum(w .* f_values);
disp(integral);

This approach uses Gaussian quadrature to accurately approximate the integral over the interval \([a, b]\).

I hope this helps!