Integrating a Function of Two Variables in MATLAB

[bewertow]

Hey guys,

I have this function:

f(r,z) = r*(1 + g(r,z))

The function g(r,z) is a modification of the student t-distribution in z, where the degrees of freedom depend continuously on r.

I would like to integrate this function f(r,z) from 0 to R with respect to r.

Unfortunately Maple could not find the integral, so I would like to do this numerically in MATLAB.

I have no clue where to start though. I've integrated a function of one variable in MATLAB before, but only with constant limits.

Any help would be greatly appreciated!

 

[mmwave]

Hi there,

Thank you for sharing your function and problem with us. It sounds like an interesting and challenging task. Here are some steps you can take to solve this problem using MATLAB:

1. Define the function g(r,z) in MATLAB: You can do this by writing a separate function file or by using the "inline" function in MATLAB. Make sure the function takes in two inputs, r and z, and outputs a single value.

2. Define the function f(r,z) in MATLAB: Similar to step 1, you can define the function f(r,z) using the "inline" function or by creating a separate function file. The function should take in r and z as inputs and output a single value, which is the result of the multiplication between r and (1 + g(r,z)).

3. Use the "integral" function: MATLAB has a built-in function called "integral" that can numerically evaluate integrals. You can use this function to integrate your function f(r,z) with respect to r. The syntax for this function is: integral(@(r)f(r,z),0,R), where R is the upper limit of integration and f(r,z) is the function you defined in step 2. This will give you the numerical value of the integral.

4. Use a loop to vary R: Since R is a variable in your function, you can use a loop to vary its value and integrate the function for different values of R. This will give you a range of numerical values for the integral, which you can then use to analyze the behavior of the function.

I hope this helps you get started with solving your problem. If you encounter any difficulties or have any further questions, please don't hesitate to reach out for help. Good luck!