Kezdőlap
Véletlen lap
Közelben
Bejelentkezés
Beállítások
Adományok
A Wikipédiáról
Jogi nyilatkozat
Keresés
Szerkesztő
:
Borbal/piszkozat
Nyelv
Lap figyelése
Szerkesztés
y
=
f
(
x
1
,
x
2
,
.
.
.
,
x
m
)
{\displaystyle y=f(x_{1},x_{2},...,x_{m})}
I
=
∬
…
∫
S
f
(
x
1
,
x
2
,
.
.
.
,
x
m
)
d
x
1
d
x
2
…
d
x
m
{\displaystyle I=\iint \dots \int _{S}\;f(x_{1},x_{2},...,x_{m})\mathrm {d} x_{1}\mathrm {d} x_{2}\dots \mathrm {d} x_{m}}
a
i
≤
x
i
≤
A
i
(
i
=
1
,
2
,
…
,
m
)
{\displaystyle a_{i}\leq x_{i}\leq A_{i}\quad (i=1,2,\dots ,m)}
x
i
=
a
i
+
(
A
i
−
a
i
)
ξ
i
{\displaystyle x_{i}=a_{i}+(A_{i}-a_{i})\xi _{i}}
0
≤
ξ
i
≤
1
(
i
=
1
,
2
,
…
,
m
)
{\displaystyle 0\leq \xi _{i}\leq 1\quad (i=1,2,\dots ,m)}
D
(
x
1
,
x
2
,
.
.
.
,
x
m
)
D
(
ξ
1
,
ξ
2
,
.
.
.
,
ξ
m
)
=
|
A
1
−
a
1
0
⋯
0
0
A
2
−
a
2
⋯
0
⋮
⋮
⋱
⋮
0
0
⋯
A
m
−
a
m
|
=
(
A
1
−
a
1
)
(
A
2
−
a
2
)
…
(
A
m
−
a
m
)
{\displaystyle {\frac {D(x_{1},x_{2},...,x_{m})}{D(\xi _{1},\xi _{2},...,\xi _{m})}}={\begin{vmatrix}A_{1}-a_{1}&0&\cdots &0\\0&A_{2}-a_{2}&\cdots &0\\\vdots &\vdots &\ddots &\vdots \\0&0&\cdots &A_{m}-a_{m}\\\end{vmatrix}}=(A_{1}-a_{1})(A_{2}-a_{2})\dots (A_{m}-a_{m})}
I
=
∬
…
∫
σ
F
(
ξ
1
,
ξ
2
,
.
.
.
,
ξ
m
)
d
ξ
1
d
ξ
2
…
d
ξ
m
{\displaystyle I=\iint \dots \int _{\sigma }\;F(\xi _{1},\xi _{2},...,\xi _{m})\mathrm {d} \xi _{1}\mathrm {d} \xi _{2}\dots \mathrm {d} \xi _{m}}
F
=
(
ξ
1
,
ξ
2
,
.
.
.
,
ξ
m
)
=
(
A
1
−
a
1
)
(
A
2
−
a
2
)
…
(
A
m
−
a
m
)
f
(
a
1
+
(
A
1
−
a
1
)
ξ
1
,
a
2
+
(
A
2
−
a
2
)
ξ
2
,
…
,
a
m
+
(
A
m
−
a
m
)
ξ
m
)
{\displaystyle F=(\xi _{1},\xi _{2},...,\xi _{m})=(A_{1}-a_{1})(A_{2}-a_{2})\dots (A_{m}-a_{m})f(a_{1}+(A_{1}-a_{1})\xi _{1},a_{2}+(A_{2}-a_{2})\xi _{2},\dots ,a_{m}+(A_{m}-a_{m})\xi _{m})}
ξ
=
(
ξ
1
,
ξ
2
,
…
,
ξ
m
)
{\displaystyle {\boldsymbol {\xi }}=(\xi _{1},\xi _{2},\dots ,\xi _{m})}
d
σ
=
d
ξ
1
d
ξ
2
…
d
ξ
m
{\displaystyle \mathrm {d} {\boldsymbol {\sigma }}=\mathrm {d} \xi _{1}\mathrm {d} \xi _{2}\dots \mathrm {d} \xi _{m}}
{\displaystyle }
I = \iint\dots \int_\sigma \;F(\boldsymbol{\xi})\mathrm{d}\boldsymbol{\sigma} </math>
{\displaystyle }
{\displaystyle }
{\displaystyle }
{\displaystyle }
{\displaystyle }