Question Number 207354 by NasaSara last updated on 12/May/24
Commented by mr W last updated on 12/May/24
$${there}\:{are}\:{integrals}\:{like}\:{following} \\ $$$$\int\int...\int\int{f}\left({x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,...,{x}_{{n}} \right){dx}_{\mathrm{1}} {dx}_{\mathrm{2}} ...{dx}_{{n}} \\ $$$$\int_{{a}_{{n}} } ^{{b}_{{n}} } \int_{{a}_{{n}−\mathrm{1}} } ^{{b}_{{n}−\mathrm{1}} } ...\int_{{a}_{\mathrm{2}} } ^{{b}_{\mathrm{2}} } \int_{{a}_{\mathrm{1}} } ^{{b}_{\mathrm{1}} } {f}\left({x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,...,{x}_{{n}} \right){dx}_{\mathrm{1}} {dx}_{\mathrm{2}} ...{dx}_{{n}} \\ $$
Commented by NasaSara last updated on 12/May/24
$${i}\:{stadied}\:{double}\:{integral}\:{with}\:{changing}\:{their}\:{orders}\:{so}\:{i}\:{was}\:{wodering}\:{if}\:{dealing}\:{with}\:{quadrable}\:{integral}\:,\:{how}\:{can}\:{i}\:{change}\:{the}\:{order}\:? \\ $$
Commented by mr W last updated on 12/May/24
$${if}\:{the}\:{bounds}\:{of}\:{the}\:{integrals}\:{are} \\ $$$${constants},\:{you}\:{can}\:{change}\:{the}\:{order} \\ $$$${arbitrarily}.\:{but}\:{if}\:{the}\:{bounds}\:{of}\:{an} \\ $$$${integral}\:{are}\:{functions}\:{of}\:{an}\:{other} \\ $$$${variable},\:{then}\:{you}\:{can}\:{not}\:{change} \\ $$$${the}\:{order}\:{of}\:{the}\:{integrals}. \\ $$
Commented by mr W last updated on 12/May/24
$${but}\:{first}\:{of}\:{all}: \\ $$$${please}\:{don}'{t}\:{write}\:{a}\:{whole}\:{post}\:{in} \\ $$$${a}\:{single}\:{line}!\:{such}\:{posts}\:{are}\:{terrible} \\ $$$${to}\:{read}. \\ $$