Integration producd NaN as answer

I tried to write a function file to implement a simple integration where 't' as input must be positive.

My code:

function y = Integration(t)
%Input a value t larger than 0, it will return an intergral
if t <= 0
  disp('Input must be positive');
  y = NaN;
else
  syms x;
  y = int(-(t-x)*exp(-(t-x))*(t-x>=0)*x^2*exp(-x)*sin(x)*(x>=0));
end
end %end of Integration2

But this code keep giving me NaN when I input postive numbers. Could someone kindly explain? Thanks!

Answer 1

[Star Strider]

First, ‘t’ needs to be defined as a sym object;

Second, use the convenient heaviside function to define the unit step function:

syms x t 
t = sym(5);                                                                     % Example 
y = int(-(t-x)*exp(-(t-x))*heaviside(t-x)*x^2*exp(-x)*sin(x)*heaviside(x));

This produces an expression for ‘y’ incorporating heaviside terms, since ‘x’ is not defined numerically.

I am not certain what result you want. At the very least, this solves the NaN problem.

[Laze]

Thanks for your response! What I wanted to do is to a function 'Integration' that can calculate the above formula. I checked the definition of heaveside, it's kinda different from a unit step function because at x=0, heavside(x)=1/2 while u(x) should equal to 1.

Besides, by trying your revision, the problem of NaN has been solved but I still could not get a numerical result rather than the above formular with t substituted by my input. Could you tell me why this is happening? Thanks a lot!

[Star Strider]

My pleasure.

The ‘unit step function’ is defined as the Heaviside function.

Answer 2

[Pal Szabo]

I think you should delete the >=0 parts from line 8. Like this:

 y = Integration(2)
 function y = Integration(t)
 %Input a value t larger than 0, it will return an intergral
 if t <= 0
   disp('Input must be positive');
   y = NaN;
 else
   syms x
   y = int(-(t-x)*exp(-(t-x))*(t-x)*x^2*exp(-x)*sin(x)*(x));
 end
 end %end of Integration2

If you want numerical result, I think you should specify the value of x.