Triangle Inequality, Integrals

[psholtz]

Is it true in general that:

$$|\int f(x)dx| < \int |f(x)|dx$$

Not sure if "Triangle Inequality" is the right word for that, but that seems to be what's involved.

 

[mathman]

It is true in general simply because -|f(x)|≤f(x)≤|f(x)|.