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Question Number 207354 by NasaSara last updated on 12/May/24

Commented by mr W last updated on 12/May/24

$t h e r e a r e i n t e g r a l s l i k e f o l l o w i n g$ $\int \int . . . \int \int f (x_{1}, x_{2}, . . ., x_{n}) {d x}_{1} {d x}_{2} . . . {d x}_{n}$ $\int_{a_{n}}^{b_{n}} \int_{a_{n - 1}}^{b_{n - 1}} . . . \int_{a_{2}}^{b_{2}} \int_{a_{1}}^{b_{1}} f (x_{1}, x_{2}, . . ., x_{n}) {d x}_{1} {d x}_{2} . . . {d x}_{n}$
Commented by NasaSara last updated on 12/May/24

$i s t a d i e d d o u b l e i n t e g r a l w i t h c h a n g i n g t h e i r o r d e r s s o i w a s w o d e r i n g i f d e a l i n g w i t h q u a d r a b l e i n t e g r a l, h o w c a n i c h a n g e t h e o r d e r ?$
Commented by mr W last updated on 12/May/24

$i f t h e b o u n d s o f t h e i n t e g r a l s a r e$ $c o n s t a n t s, y o u c a n c h a n g e t h e o r d e r$ $a r b i t r a r i l y . b u t i f t h e b o u n d s o f a n$ $i n t e g r a l a r e f u n c t i o n s o f a n o t h e r$ $v a r i a b l e, t h e n y o u c a n n o t c h a n g e$ $t h e o r d e r o f t h e i n t e g r a l s .$
Commented by mr W last updated on 12/May/24

$b u t f i r s t o f a l l :$ $p l e a s e {d o n}^{'} t w r i t e a w h o l e p o s t i n$ $a s i n g l e l i n e! s u c h p o s t s a r e t e r r i b l e$ $t o r e a d .$
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