Double Integration by Simpson's Rule | Programming Numerical Methods in MATLAB 

You're welcome. I plotted it by using Octave function surf(x,y,z). I add the red dots and symbols and other lines manually by using Paint which comes with Windows.

Thank you Youcef for the comment and question. This tutorial, like other tutorials in this channel, is educational and introduces the basic steps of the numerical method for students and professionals who study or interested in the programming of the method. On the other hand, the MATLAB library functions, such as int and int2, are more reliable for practical applications because they offer more options and are faster in execution due to pre-compiled codes they use. The only advantage of the open code in these tutorials is that they can be modified by users for more specific applications as required.

This program of double integration can be modified so that the limit set as an inline function. Two important things: (1) Since the limit is a function of y, the y values loop should be outside and x loop inside so limits are calculated for each y. (2) Values of hx should be calculated inside the outer loop of y because the limit function of y will be used to find hx at each y. If the a limit function of x, the same procedure will be applied but in opposite order.