integral 音標拼音: ['ɪntəgrəl] ['ɪnəgrəl]
n . 積分,整數
a . 整體的,整數的,積分的
n . 積分
積分,整數整體的,整數的,積分的積分
integral 積分
integral 積分 整數 整體
integral adj 1 :
existing as an essential constituent or characteristic ;
"
the Ptolemaic system with its built -
in concept of periodicity "; "
a constitutional inability to tell the truth " [
synonym : {
built -
in }, {
constitutional }, {
inbuilt },
{
inherent }, {
integral }]
2 :
constituting the undiminished entirety ;
lacking nothing essential especially not damaged ; "
a local motion keepeth bodies integral "-
Bacon ; "
was able to keep the collection entire during his lifetime "; "
fought to keep the union intact " [
synonym : {
integral }, {
entire }, {
intact }]
3 :
of or denoted by an integer n 1 :
the result of a mathematical integration ;
F (
x )
is the integral of f (
x )
if dF /
dx =
f (
x )
Fluent \
Flu "
ent \,
n .
1 .
A current of water ;
a stream . [
Obs .]
[
1913 Webster ]
2 . [
Cf .
F .
fluente .] (
Math .)
A variable quantity ,
considered as increasing or diminishing ; --
called ,
in the modern calculus ,
the {
function }
or {
integral }.
[
1913 Webster ]
Integral \
In "
te *
gral \,
a . [
Cf .
F .
int ['
e ]
gral .
See {
Integer }.]
[
1913 Webster ]
1 .
Lacking nothing of completeness ;
complete ;
perfect ;
uninjured ;
whole ;
entire .
[
1913 Webster ]
A local motion keepeth bodies integral . --
Bacon .
[
1913 Webster ]
2 .
Essential to completeness ;
constituent ,
as a part ;
pertaining to ,
or serving to form ,
an integer ;
integrant .
[
1913 Webster ]
Ceasing to do evil ,
and doing good ,
are the two great integral parts that complete this duty .
--
South .
[
1913 Webster ]
3 . (
Math .)
(
a )
Of ,
pertaining to ,
or being ,
a whole number or undivided quantity ;
not fractional .
(
b )
Pertaining to ,
or proceeding by ,
integration ;
as ,
the integral calculus .
[
1913 Webster ]
{
Integral calculus }.
See under {
Calculus }.
[
1913 Webster ]
Integral \
In "
te *
gral \,
n .
1 .
A whole ;
an entire thing ;
a whole number ;
an individual .
[
1913 Webster ]
2 . (
Math .)
An expression which ,
being differentiated ,
will produce a given differential .
See differential {
Differential },
and {
Integration }.
Cf . {
Fluent }.
[
1913 Webster ]
{
Elliptic integral },
one of an important class of integrals ,
occurring in the higher mathematics ; --
so called because one of the integrals expresses the length of an arc of an ellipse .
[
1913 Webster ]
106 Moby Thesaurus words for "
integral ":
a certain ,
aggregate ,
algorismic ,
algorithmic ,
aliquot ,
all ,
all -
embracing ,
all -
inclusive ,
an ,
any ,
any one ,
atomic ,
basic ,
cardinal ,
complete ,
component ,
composite ,
comprehensive ,
constituent ,
decimal ,
differential ,
digital ,
either ,
elemental ,
elementary ,
entire ,
entity ,
essential ,
even ,
exclusive ,
exhaustive ,
exponential ,
figural ,
figurate ,
figurative ,
finite ,
formative ,
fractional ,
full ,
fundamental ,
gross ,
holistic ,
imaginary ,
impair ,
impossible ,
inclusive ,
individual ,
indivisible ,
infinite ,
intact ,
integrant ,
integrate ,
integrated ,
intrinsic ,
irrational ,
irreducible ,
logarithmic ,
logometric ,
lone ,
monadic ,
monistic ,
negative ,
numeral ,
numerary ,
numerative ,
numeric ,
odd ,
omnibus ,
one ,
one and indivisible ,
ordinal ,
pair ,
perfect ,
positive ,
possible ,
prime ,
radical ,
rational ,
real ,
reciprocal ,
rolled into one ,
simple ,
single ,
singular ,
sole ,
solid ,
solitary ,
sound ,
submultiple ,
sum ,
surd ,
system ,
total ,
totality ,
transcendental ,
unanalyzable ,
undivided ,
unified ,
uniform ,
unique ,
unitary ,
united ,
universal ,
unqualified ,
utter ,
whole
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calculus - Integration by parts on definite integral - Mathematics . . . I have an integral, $$ I = \int_a^b x f (x) dx $$ and I would like to express this in terms of $\int_a^b f (x) dx$ if possible, but I don't see how integration by parts will help here
What does it mean for an integral to be convergent? The noun phrase "improper integral" written as $$ \int_a^\infty f (x) \, dx $$ is well defined If the appropriate limit exists, we attach the property "convergent" to that expression and use the same expression for the limit
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