1/3 simpson rule for integration in matlab

To use the 1/3 Simpson's rule for numerical integration in MATLAB, you can follow these steps:

1. Define the function you want to integrate. Let's assume you have a function called f(x) that you want to integrate over a certain interval.

2. Determine the boundaries of the interval you want to integrate over. Let's say the lower bound is a and the upper bound is b.

3. Decide on the number of subintervals you want to divide the interval into. The number of subintervals should be even for the 1/3 Simpson's rule. Let's call this number n.

4. Calculate the width of each subinterval using the formula h = (b - a) / n.

5. Set up an array to store the function values at the endpoints of each subinterval. Let's call this array y.

6. Use a loop to evaluate the function at the endpoints of each subinterval and store the values in the y array.

   main.m
   for i = 1:n+1
       x(i) = a + (i - 1) * h;
       y(i) = f(x(i));
   end
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7. Apply the 1/3 Simpson's rule formula to calculate the approximate integral.

   main.m
   integral = (h / 3) * (y(1) + 4 * sum(y(2:2:end-1)) + 2 * sum(y(3:2:end-2)) + y(end));
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   Here, y(1) and y(end) are the function values at the first and last points of the interval, respectively. sum(y(2:2:end-1)) calculates the sum of the function values at the odd-indexed points, and sum(y(3:2:end-2)) calculates the sum of the function values at the even-indexed points.

8. Print the value of the approximate integral.

   main.m
   disp(integral);
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That's it! You have now implemented the 1/3 Simpson's rule for numerical integration in MATLAB.

Note: Make sure to define the function f(x) beforehand or replace it with the actual function you want to integrate in step 1.