Need Help with Numerical Integration in MATLAB

[n0_3sc]

Here is an integral (similar in form to the one) I want to evaluate:
$$ \int_{r_1}^{r_2} R \left\{ \int_{x_1}^{x_2} Y(x,R)\, dx \right\}^2\,dR $$
This is my approach - please correct me because I don't think it's right:
I treat R as a constant and evaluate the inner integral over some vector of x (using the function "trapz" in MATLAB)
I do the same thing again for another value of R (until the range of R values are done). Ending up with an array of values for the inner integral. (Where each element corresponds to the integral of a particular value of R).
Lastly, I evaluate the outer integral (with "trapz") over the same vector of R but for each value of the inner integral.

What do you think?

 

[NateD]

Is this the correct approach?No, this is not the correct approach. The correct approach would be to use the method of substitution to first evaluate the inner integral for all values of R, and then to evaluate the outer integral with the results of the inner integral. This can be done by setting the inner integral equal to a new variable, say U, and then substituting U back into the outer integral.

 

[oswaler]

Your approach seems correct. Since the integral is in the form of nested integrals, it would be best to use the "trapz" function in MATLAB to evaluate each integral separately. First, you can create a vector of evenly spaced values for R, and then use a loop to evaluate the inner integral for each value of R. This will give you an array of values for the inner integral. Then, you can use the "trapz" function again to evaluate the outer integral over the same vector of R, using the array of values for the inner integral as the function to be integrated. This will give you the final result of the integral. Just make sure to use appropriate limits for the inner and outer integrals and to check your results with other methods to ensure accuracy.