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

Improper Integral on Closed Interval Unbounded Above: Also known as

When presenting an improper integral on an unbounded closed interval $\hointr a \to$, it is common to abuse notation and write:

$\ds \int_a^\infty \map f t \rd t$

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

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 15$: Definition of a Definite Integral: $15.3$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): infinite integral (improper integral)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): infinite integral (improper integral)