Finding a constant to make a valid pdf Let $f(x) = c\cdot 2^{-x^2}$. How do I find a constant $c$ such that the integral evaluates to $1$?

Hint: Rewrite
$$f(x) = c \,[e^{\ln(2)}]^{-x^2} = c\, e^{-x^2\ln(2)}$$
and try to exploit the following integral together with some change of variable:
$$
\int^{\infty}_0 e^{-x^2} \,dx = \frac{\sqrt{\pi}}{2}
$$
