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

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Rikesh
Rikesh 2022-8-10
编辑： Walter Roberson 2025-1-20
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  1 个评论
Mahesh
Mahesh 2024-12-9
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

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Avni Agrawal
Avni Agrawal 2025-1-20
编辑：Walter Roberson 2025-1-20
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!

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