Limits of integration

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Topics in calculus

Fundamental theorem
Limits of functions
Continuity
Vector calculus
Matrix calculus
Mean value theorem
Differentiation

Product rule
Quotient rule
Chain rule
Implicit differentiation
Taylor's theorem
Related rates
List of differentiation identities
Integration

Lists of integrals
Improper integrals
Integration by:
parts, disks, cylindrical
shells, substitution,
trigonometric substitution,
partial fractions, changing order

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 [a, b] are the real numbers a and b.

[edit] Improper integrals

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

and

\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

or

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

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

[edit] See also

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