# Integral Question

1. Sep 17, 2004

### 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!

2. Sep 17, 2004

### 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).

3. Sep 17, 2004

### Tide

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.

4. Sep 18, 2004

### PrudensOptimus

5. Sep 18, 2004

### Tide

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

6. Sep 18, 2004

### Lonewolf

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

7. Sep 18, 2004

### PrudensOptimus

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