MATLAB: Error when trying to integrate over step function

Question

I am trying to integrate a step function and I keep getting error messages.

Here is my code:

>> integral(step_fun,5,7)
Error using step_fun (line 4)
Not enough input arguments.

The step_fun is defined in a separate code file as:

function y = step_fun(x)
y = 0; 
if x >= 0
    y = 1;
end;
end

If I try:

func=@(t) step_fun(t)
integral(func,5,7)

I got:

Error using integralCalc/finalInputChecks (line 515)
Output of the function must be the same size as the input. If FUN is an
array-valued integrand, set the 'ArrayValued' option to true.
Error in integralCalc/iterateScalarValued (line 315)
                finalInputChecks(x,fx);
Error in integralCalc/vadapt (line 132)
            [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);
Error in integralCalc (line 75)
        [q,errbnd] = vadapt(@AtoBInvTransform,interval);
Error in integral (line 88)
Q = integralCalc(fun,a,b,opstruct);

What does this mean? Thank you.

Answer 1

integral() passes in a vector of values and expects one result for each element of the vector. You need to vectorize:

function y = step_fun(t)
  y = zeros(size(t));
  y(t>=0) = 1;

Or more compactly,

function y = step_fun(t)
   y = t >= 0;

which can be done as

step_fun = @(t) t >= 0;