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

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

When presenting an improper integral on $\R$, it is common to abuse notation and write:

$\ds \int_{-\infty}^\infty \map f t \rd t$

which is understood to mean exactly the same thing as $\ds \int_{\mathop \to -\infty}^{\mathop \to + \infty} \map f t \rd t$.

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 15$: Definition of a Definite Integral: $15.4$
• 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 18$: Definite Integrals: Definition of a Definite Integral: $18.4$