# How do I find the constant in this pdf?

Suppose I have the following probability density function.

$$f(x) = \begin{cases}ce^{-\frac x{200}}&\mathrm{\ if\ } 0<x<\infty\\ 0&\mathrm{\ if\ }x\le0\end{cases}?$$

How do I find $c$? Currently, I have the following.

$$\int_0^\infty ce^{-\frac x{200}}dx = 1$$

$$\lim_{x\to\infty} -200ce^{-\frac x{200}} + 200c = 1$$

$$c = \frac1{200}$$

Is this right?

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So we want to choose $c$ so that $$\int_0^\infty ce^{-x/200}\, dx=1.$$
An antiderivative of $ce^{-x/200}$ is $-200ce^{-x/200}$. So our definite integral is $200c$. It follows that $c=1/200$.