Last Updated：2025/11/19
(mathematics) One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof.
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integral
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Source Word
integral
IPA(Pronunciation)
Noun
specifically
historical
obsolete
(mathematics)
One
of
the
two
fundamental
operations
of
calculus
(the
other
being
differentiation),
whereby
a
function's
displacement,
area,
volume,
or
other
qualities
arising
from
the
study
of
infinitesimal
change
are
quantified,
usually
defined
as
a
limiting
process
on
a
sequence
of
partial
sums.
Denoted
using
a
long
s:
∫,
or
a
variant
thereof.
Japanese Meaning
積分（数学）: 関数の変位、面積、体積などを求める計算手法で、微小変化の分析から部分和列の極限を取ることで求められる微分積分学の基本操作の一つ。
Sense（1）
(mathematics)
One
of
the
two
fundamental
operations
of
calculus
(the
other
being
differentiation),
whereby
a
function's
displacement,
area,
volume,
or
other
qualities
arising
from
the
study
of
infinitesimal
change
are
quantified,
usually
defined
as
a
limiting
process
on
a
sequence
of
partial
sums.
Denoted
using
a
long
s:
∫,
or
a
variant
thereof.
Sense（2）
Sense（3）
(mathematics)
A
definite
integral:
the
result
of
the
application
of
such
an
operation
onto
a
function
and
a
suitable
subset
of
the
function's
domain:
either
a
number
or
positive
or
negative
infinity.
In
the
former
case,
the
integral
is
said
to
be
finite
or
to
converge;
in
the
latter,
the
integral
is
said
to
diverge.
In
notation,
the
domain
of
integration
is
indicated
either
below
the
sign,
or,
if
it
is
an
interval,
with
its
endpoints
as
sub-
and
super-scripts,
and
the
function
being
integrated
forming
part
of
the
integrand
(or,
generally,
differential
form)
appearing
in
front
of
the
integral
sign.
Sense（4）
（ plural ）
