Szerkesztő:Borbal/piszkozat

$y=f(x_{1},x_{2},...,x_{m})$

$I=\iint \dots \int _{S}\;f(x_{1},x_{2},...,x_{m})\mathrm {d} x_{1}\mathrm {d} x_{2}\dots \mathrm {d} x_{m}$

$a_{i}\leq x_{i}\leq A_{i}\quad (i=1,2,\dots ,m)$

$x_{i}=a_{i}+(A_{i}-a_{i})\xi _{i}$

$0\leq \xi _{i}\leq 1\quad (i=1,2,\dots ,m)$

${\frac {D(x_{1},x_{2},...,x_{m})}{D(\xi _{1},\xi _{2},...,\xi _{m})}}={\begin{vmatrix}A_{1}-a_{1}&0&\cdots &0\\0&A_{2}-a_{2}&\cdots &0\\\vdots &\vdots &\ddots &\vdots \\0&0&\cdots &A_{m}-a_{m}\\\end{vmatrix}}=(A_{1}-a_{1})(A_{2}-a_{2})\dots (A_{m}-a_{m})$

$I=\iint \dots \int _{\sigma }\;F(\xi _{1},\xi _{2},...,\xi _{m})\mathrm {d} \xi _{1}\mathrm {d} \xi _{2}\dots \mathrm {d} \xi _{m}$

$F=(\xi _{1},\xi _{2},...,\xi _{m})=(A_{1}-a_{1})(A_{2}-a_{2})\dots (A_{m}-a_{m})f(a_{1}+(A_{1}-a_{1})\xi _{1},a_{2}+(A_{2}-a_{2})\xi _{2},\dots ,a_{m}+(A_{m}-a_{m})\xi _{m})$

${\boldsymbol {\xi }}=(\xi _{1},\xi _{2},\dots ,\xi _{m})$

$\mathrm {d} {\boldsymbol {\sigma }}=\mathrm {d} \xi _{1}\mathrm {d} \xi _{2}\dots \mathrm {d} \xi _{m}$

${\displaystyle }$ I = \iint\dots \int_\sigma \;F(\boldsymbol{\xi})\mathrm{d}\boldsymbol{\sigma} </math>

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