Can Any Function Satisfy a General Integral Equation?

[Vorde]

Is there any function such that:
$_{-∞}$$\int$$^{∞}$f(x) dx
Is any integer except 0 and ∞?

 

[omkar13]

f(x) can be impulse function

 

[DeadOriginal]

I'm not sure what omkar meant by impulse function but if f(x)=$\frac{1}{1+x^2}$, the integral will not equal 0 or ∞.

 

[Vorde]

I looked it up, apparently is an equation that satisfies the statement that the integral from -∞ to ∞ is 1, but because of the way it's defined it isn't actually a function.

 

[phyzguy]

Is there any function such that:
$_{-∞}$$\int$$^{∞}$f(x) dx
Is any integer except 0 and ∞?

There are an infinite number of such functions. For example:
$$\int^\infty_{-\infty}e^{-x^2}dx = \sqrt{\pi}$$
so if:
$$f(x) = \frac{7}{\sqrt\pi}e^{-x^2}$$
then:
$$\int^\infty_{-\infty}f(x)dx = 7$$
There are lots of functions like this that one can play this game with.

 

[DeadOriginal]

I looked it up, apparently is an equation that satisfies the statement that the integral from -∞ to ∞ is 1, but because of the way it's defined it isn't actually a function.

Ohhhh. That is very interesting. This is the first time I have ever heard of that.

There are an infinite number of such functions. For example:
$$\int^\infty_{-\infty}e^{-x^2}dx = \sqrt{\pi}$$
so if:
$$f(x) = \frac{7}{\sqrt\pi}e^{-x^2}$$
then:
$$\int^\infty_{-\infty}f(x)dx = 7$$
There are lots of functions like this that one can play this game with.

Cool! That looks fun lol.