M-files to solve numerical integration

[mazi]

Homework Statement

Numerical integration using MATLAB m-files
Find the area under the curve of:
using trapezium rule

Homework Equations

g(x) = x^2 from x=0 to x=2
Area of a trapezium = h/2(a+b)

The Attempt at a Solution

 

[marcusl]

Please attempt a solution and share it with us. Physics Forums does not do your homework for you.

 

[mazi]

I am actually trying out something. it is not my homework and i have no idea since i am new to MATLAB software. can't figure out how to program the mfile

 

[marcusl]

You can use the command "trapz", look it up in the help files. It integrates a numerical sequence using the trapezoidal rule.

 

[DeeNos]

To solve this numerical integration problem using MATLAB m-files, we can first define the function g(x) = x^2 using the code "g = @(x) x.^2". Then, we can use the trapezium rule, which states that the area under the curve can be approximated by dividing the interval into small trapeziums and adding their areas together. This can be implemented in MATLAB using the code "h/2*(g(a)+g(b))", where h is the step size and a and b are the limits of integration. Finally, we can use a loop to iterate through different values of h and calculate the area under the curve for each, until we reach a desired level of accuracy. This approach allows for a more accurate and efficient solution to the numerical integration problem compared to manual calculations. Additionally, using m-files in MATLAB allows for easy modification of the code for different functions and integration methods.