Originally Posted by
Chris L T521 For this to be a pdf, $\displaystyle \int_{-\infty}^{\infty}P\left(x\right)\,dx=1$
Thus, solve the equation $\displaystyle \int_{-\infty}^{\infty} k\left(1-x^3\right)\,dx=1\implies \int_0^1 k\left(1-x^3\right)\,dx=1$ for k.
Can you take it from here?