Definition:Improper Integral on Interval Unbounded Above and Below/Also defined as

Improper Integral on Interval Unbounded Above and Below: Also defined as

An improper integral defined over $\R$ can also be seen defined as:

$\ds \int_{\mathop \to -\infty}^{\mathop \to +\infty} \map f t \rd t := \lim_{\substack {b \mathop \to \infty \\ a \mathop \to -\infty} } \int_a^b \map f t \rd t$

but this can be argued as being more opaque and hence less intuitively easy to grasp accurately.

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 15$: Definition of a Definite Integral: $15.4$