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I've been trying to figure out to say something about the product of two functions that I know the integral to. More specifically, some function $K$ and some linear function $a\cdot x$. I know the following:

$\int_{\Gamma} K \; ds_x = 1$

Is it possible to say anything about:

$\int_{\Gamma} K\cdot x \; ds_x = $ ?

I tried alot of standard methods like partial integration, however $K$ is a very tedious function to work with in this case. Any help is greatly appreciated.

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Unless you know something more about $K$, you can't say much at all. If all you know is $K\ge0$, all you can say is $\int Kx\le\max_{x{\rm\ in\ }\Gamma}|x|$ and a similar lower bound.

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    Now I believe it +1 ;)2012-02-24