Integral Question: Deriving Formula for $\int|f(x)|dx$

[Paul]

Hello everyone! Can anyone tell me a formula (or a way to derive) this integral?
\int|f(x)|dx
where f(x) is a real, continuous function of x in the vector space C^\infty. So far, all I've figured out is that odd-order integrations are related to the signum function.
Thanks!

 

[PrudensOptimus]

Derive or find the area under |f(x)|?

|f(x)| = f(x), if x >=0; -f(x), if x<0

so &Int; |f(x)| dx has 2 solutions: F(x), and -F(X), where F(X) is the antiderivative of f(x).

 

[Tide]

Derive or find the area under |f(x)|?

|f(x)| = f(x), if x >=0; -f(x), if x<0

so &Int; |f(x)| dx has 2 solutions: F(x), and -F(X), where F(X) is the antiderivative of f(x).

No, |f(x)| = f(x) if f(x) >= 0 and -f(x) if f(x) < 0.

I recommend breaking up the integral into separate domains as I've indicated and integrating piecewise.

 

[PrudensOptimus]

No, |f(x)| = f(x) if f(x) >= 0 and -f(x) if f(x) < 0.

I recommend breaking up the integral into separate domains as I've indicated and integrating piecewise.

Stop repeating my answers :p

 

[Tide]

Stop repeating my answers :p

LoL! Man, I've just GOTTA get some reading glasses!

 

[Lonewolf]

He wasn't repeating your answers. Prudens used x, while Tide correctly used f(x).

 

[PrudensOptimus]

what i really meant was f(x)... but i was thinking about beer.