\begin{definition}[Definition:Improper Integral/Unbounded Closed Interval/Unbounded Above]
Let $f$ be a real function which is continuous on the unbounded closed interval $\hointr a \to$.
Then the improper integral of $f$ over $\hointr a \to$ is defined as:
:$\ds \int_a^{\mathop \to +\infty} \map f t \rd t := \lim_{\gamma \mathop \to +\infty} \int_a^\gamma \map f t \rd t$
\end{definition}