What's the Origin of This Integral Inequality?

[philosophking]

I know this is probably a gross generalization of what the actual inequality states, but I'm wondering if someone can tell me the origin of this integral inequality (or something resembling it :/ ):

$$|\int f(x)| \leq \int|f(x)|$$

This is my first time using latex, so I hoped that turned out ok. Any suggestions on that too would be appreciated! Thanks.

 

[DoubleMike]

I don't understand your question...

the left side just takes the absolute value of the area under f(x), which could well be negative. As for the right side, it will count a negative f(x) as positive... if it's applied to a velocity function, it would give the total distance traveled rather than displacement for example.

 

[Crosson]

$$|\int f(x)| \leq \int|f(x)|$$

This is not a terribly interesting equality, I am sure that you could form a proof. I can only guess that you are trying to discuss the cauchy-schwarz inequality:

http://mathworld.wolfram.com/SchwarzsInequality.html

Which is reasonably famous but very uninteresting.

 

[Data]

It's just an application of the triangle inequality.