I need to find 10th percentile of random variable X with PDF defined with:

$\displaystyle

f(x) = \left\{\begin{array}{cc}c(x-x^3)&0< x < 1\\0&x\le 0 \vee x\ge 1 \end{array}\right.

$

where $\displaystyle c\in \mathbb{R}$ is const that should be found too.

By integrating f from 0 to $\displaystyle x$ I got cumulative dist. function $\displaystyle F(x) = c \frac{2x^2 - x^4}{4}$, so $\displaystyle c=4$.

First, is this approach OK, and second, how can I calculate required percentile?

Thanks guys