# How to multiply function handles?

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Max on 22 Jan 2016
Commented: Tiago Araujo on 24 Jun 2021
Hello,
I would like to calculate and to plot the following equation:
f(t,x) = (beta_hat*s(t,x)*[I(t,x)]^(beta_hat-1))*exp(-[I(t,x)]^beta_hat)
where:
s(t,x): step-function(330 for x=[0;2000])
(350 for x=[2000;3000])
(390 for x=[3000;4000])
I(t,x): Integral(exp(-B_hat/x(u))/C_hat)) from x=0 to t
beta_hat, C_hat and B_hat are known parameters
My MATLAB-script looks like that:
beta_hat = 4.2915822
B_hat = 1861.6186657
C_hat = 58.9848692
%%Step-function x(t)
syms t
y(t) = (exp(-B_hat/((heaviside(t)-heaviside(t-2000))*(330)+(heaviside(t-2000)-heaviside(t-3000))*(350)+...
(heaviside(t-3000)-heaviside(t-4000))*(390))))/C_hat;
fnum=matlabFunction(y);
Inum=@(x)integral(fnum,0,x);
f = @(x)(beta_hat*fnum(x).*Inum(x).^(beta_hat-1)).*exp(-(Inum(x).^beta_hat))
ezplot(f,[0,14000])
But if I plot my function f the figure isn´t right. There should be a smooth curve, similar to the bell-shaped curve.
Does anybody recognize my fault?

Walter Roberson on 22 Jan 2016
What value are you assuming that heaviside(0) has?
As you are working with the Symbolic toolbox anyhow, have you considered doing a symbolic integration with int() instead of changing to a numeric function and using integral() ?
Walter Roberson on 22 Jan 2016
heaviside(x) is defined to be 0 for x < 0,, and is defined to be 1 for x > 0. You cannot have heaviside(t=4000) be 390 .
The value of heaviside(x) for x = 0 is not precisely defined. In some systems, heaviside(0) is undefined. In some systems, heaviside(0) is 1/2 . In some systems, heaviside(0) is 0. In some systems, heaviside(0) is 1.
As of R2015a, you can use the new sympref() to control the value that is used for heaviside(0)
Remember, no matter what value you use, heaviside is discontinuous, so you should avoid using numeric integration with it, unless you split your integral up into disjoint ranges at each boundary, integrate each separately, and total the results.

Tiago Araujo on 24 Jun 2021
I need to do a integral with a function by combining two functions, something like this:
syms q r
x(q,r) = q + 2*r;
y(q,r) = q*9 + r;
G = @(q,r) x+y
integral2(G,1,2,1,2)
It is only a example, my real problem is much more complex. How can i do that?
Tiago Araujo on 24 Jun 2021
You're great! Thanks, matlabFunction solved my problem! I didnt know this function.