Solving Integrals: q(x) on [0,1], xq(x), x^2q(x)

[noowutah]

Let q be a continuous function on [0,1] for which

\int_{0}^{1}q(x)dx=1

How do you solve the integrals

\int_{0}^{1}xq(x)dx

and

\int_{0}^{1}x^2q(x)dx

This is a real life (well, game theory) problem.

 

[LCKurtz]

Use tex tags instead of code tags and a \, like this (click on it)

$$\int_{0}^{1}x^2q(x)dx$$

The answer is, you don't. Just knowing the area under a curve doesn't determine either its first or second moments. You need more info.

 

[noowutah]

That's too bad, but good to know. Thanks.