Limits of integration

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

 \int_a^b f(x) \, dx

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

Improper integrals[edit]

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

 \lim_{z \rightarrow a^+} \int_z^b f(x) \, dx


 \lim_{z \rightarrow b^-} \int_a^z f(x) \, dx

again being a and b. For an improper integral

 \int_a^\infty f(x) \, dx


 \int_{-\infty}^b f(x) \, dx

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

See also[edit]