I have this exercise which I don't know if I solved it right:
I have to calculate $c \in \mathbb{R}$ so that the following function is a PDF in $\mathbb{R}$.
$ f(x):=\left\{\begin{matrix} & ce^{-a^2x} & 0<x\\ & 0 & otherwise \end{matrix}\right.$ Where $a\neq0$
I have done the following:
$c\int_0^\infty e^{-a^2x}dx=1=\frac{-c}{a^2}[\frac{1}{e^{a^2x}}]_0^\infty=\frac{-c}{a^2}(-1)=> c=a^2$
Is my solution right?