Limits of integration

Differential calculus
Derivative Change of variables Implicit differentiation Taylor's theorem Related rates Rules and identities: Power rule, Product rule, Quotient rule, Chain rule

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

Vector calculus
Gradient Divergence Curl Laplacian Gradient theorem Green's theorem Stokes' theorem Divergence theorem

Multivariable calculus
Matrix calculus Partial derivative Multiple integral Line integral Surface integral Volume integral Jacobian

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

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

$\lim_{z \rightarrow a^%2B} \int_z^b f(x) \, dx$

and

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

again being a and b. For an improper integral

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

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

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