34Finding $c$ for a density

$\displaystyle f(x) = cx^2$ on $\displaystyle [0, 3]$ ($\displaystyle 0$ elsewhere) is a probability density. Find $\displaystyle c$.

A density needs total area 1 under it, so integrate cx² from 0 to 3 and set it to 1. That gives 9c = 1, so c = 1/9. Check: 9·(1/9) = 1.