Is it possible to double integrate a function with three variables?

I have a function interms of three variables. Can I integarte with respect to two variables in matlab?

[Sandra Maria Cherian]

I need to integrate both numeraically.

Answer 1

[Tejas Jayashankar]

Hi Sandra,

It is possible to perform integration with respect to only 2 variables in a 3 dimensional space. Consider the integral of the function f(x, y, z) = xyz, where x ranges from 0 to y/2 and y ranges from 0 to 1.

You can perform integration using the int or integral function in MATLAB. The int function performs indefinite and definite integration over symbolic variables whereas the integral, integral2 and integral3 functions perform definite integrals. Check the documentation for further information.

Coming back to the integral mentioned above, one can implement it as follows in MATLAB:

syms x y z
f = x * y * z;
int(int(f, x, [0 y/2]), y, [0 1])

I am declaring x, y, z as symbolic variables and first performing the inner integral with respect to x and then the outer integral with respect to y. As expected the answer returned is z/32.

Also look at this answer: https://www.mathworks.com/matlabcentral/answers/174009-symbolic-integration-vs-numerical-integration

[Sandra Maria Cherian]

I tried the code, but whenever I run that code my system get hang and automatically close all applications running. Do you have any solution for this?