Why Does int() of rectangularPulse Return NaN?

syms t real
x(t) = rectangularPulse(0,1,t);
int(x(t),t,0,5)

ans = 

1

int(x(t),t,0,inf)

ans = 

NaN

int(x(t),t,-10,10)

ans = 

1

int(x(t),t,-inf,inf)

ans = 

NaN

Any ideas why those two cases return NaN?

[Paul]

Fixed in 2022a

syms t real
x(t) = rectangularPulse(0,1,t);
int(x(t),t,0,inf)

ans = 

1

int(x(t),t,-inf,inf)

ans = 

1

int(rectangularPulse(0,1,t),-2,inf)

ans = 

1

Answer 1

[Walter Roberson]

Work-around:

syms b x t real
assume(b>=0)
y(t) = rectangularPulse(x,1,t)

y(t) = 

z = int(y,t,0,b)

z = 

limit(z, b, inf)

ans = 

[Paul]

Seems like this should be pretty simple function for int() to deal with. Does this seem like a bug?

[Walter Roberson]

I am not sure why this is happening. You can read the internal code for rectangularPulse by using

regexprep(char(feval(symengine, 'expose', 'rectangularPulse')),'\\n','\n')

but that doesn't tell you anything about how it integrates. The symbolic integration routine is too large for me to chase through.

[Paul]

Just seems so strange because int() handles much more complex functions, which is just about any function, with ease. I'll see what Tech Support says about this.

Another interesting result:

syms t real
int(rectangularPulse(0,1,t),-inf,2)

ans = 

1

int(rectangularPulse(0,1,t),-2,inf)

ans = 

NaN

[Walter Roberson]

I have a suspicion that somewhere along the way, a dirac(0) is getting invoked.