Limits of integration

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





∫

a


b


f
(
x
)

d
x


{\displaystyle \int _{a}^{b}f(x)\,dx}
of a Riemann integrable function f defined on a closed and bounded [interval] are the real numbers



a


{\displaystyle a}
and



b


{\displaystyle b}
. The region that is bounded can be seen as the area inside



a


{\displaystyle a}
and



b


{\displaystyle b}
.
For example, the function



f
(
x
)
=

x

3




{\displaystyle f(x)=x^{3}}
is bounded on the interval



[
2
,
4
]


{\displaystyle [2,4]}






∫

2


4



x

3



d
x


{\displaystyle \int _{2}^{4}x^{3}\,dx}

with the limits of integration being



2


{\displaystyle 2}
and



4


{\displaystyle 4}
.

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