Let $f : [0, \infty) \to (0, \infty)$ be a D5482: Positive real function such that
| (i) | $\theta \in (0, \infty)$ is a D5407: Positive real number |
| (ii) | \begin{equation} f(x) = e^{- \theta x} \end{equation} |
Then
| (1) | $f$ is an D6103: Improperly Riemann integrable real function on $[0, \infty)$ |
| (2) | \begin{equation} \int^{\infty}_0 f(t) \, d t = \frac{1}{\theta} \end{equation} |