Limits of integration - Alchetron, The Free Social Encyclopedia

In calculus and mathematical analysis the limits of integration of the integral

∫ a b f ( x ) d x

of a Riemann integrable function f defined on a closed and bounded [interval] are the real numbers a and b.

Improper integrals

Limits of integration can also be defined for improper integrals, with the limits of integration of both

lim z → a + ∫ z b f ( x ) d x

and

lim z → b − ∫ a z f ( x ) d x

again being a and b. For an improper integral

∫ a ∞ f ( x ) d x

or

∫ − ∞ b f ( x ) d x

the limits of integration are a and ∞, or −∞ and b, respectively.

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