How I can integrate function if I have two variables?

Hi:

I am using trapz to integrate my function, but in my function I have two variables, what should I do if I want to integrate only one variable and keep the other one? if anyone can help me, I will be appreciate it.

Thank you

Subinuer

[Laurence Lurio]

Suppose you have f(x,y) and you want to integrate from A to B over x with y=y0. Then

y=y0
fun2=@(x)fun(x,y0)
result=integral(fun2,A,B)

Answer 1

[Star Strider]

If you have already evaluated your function and have a matrix of (x,y) values for it, you can use trapz to integrate it in the dimension you want.

Example:

f = @(x,y) 3*x.^2 + 5*y.^3;
x = 0:0.1:5;
y = 0:0.1:7;
[X, Y] = meshgrid(x,y);
fmtx = f(X,Y);
fxint = trapz(x,fmtx,2);

figure(1)
surfc(X,Y,fmtx)
grid on
xlabel('X')
ylabel('Y')

Otherwise, you need to do the integration with the Symbolic Math Toolbox:

syms x y 
f(x,y) = 3*x.^2 + 5*y.^3;
fint = int(f, x)

[Subinuer]

ok, thank you for your answer. I tried with traps, because I want to express all the function with y(one of the variable) after integrating, I don't have any value for y, after integrating I need to solve a matrix equation to find y. So do you think traps is working for me? if I use int, after integrating, it is in the syms form, how can I solve that one?

[Star Strider]

My pleasure!

However, I do not understand your function, your data, or what you want to do. You can use matlabFunction (Symbolic Math Toolbox) to create an anonymous function (or function file) from your partially-integrated function as a function of the remaining variable.

[Subinuer]

Thank you, I will try like this.

[Star Strider]

My pleasure!

[Sinipelto]

I was using "integral" function which didnt work, when I switched to this "int" function, it started working. Thanks!

[Star Strider]

My pleasure!

The trapz function integrates vectors and matrices numerically.

The integral function integrates functions numerically.

The int function integrates symbolic expressions and functions, and vpaintegral integrates them numerically.