find ∫_0 ^(+∞) [ x e^(−x) ]dx


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Question Number 37633 by math khazana by abdo last updated on 16/Jun/18

$f i n d \int_{0}^{+ \infty} [x e^{- x}] d x$
	Answered by tanmay.chaudhury50@gmail.com last updated on 16/Jun/18

	$i f [{x e}^{- x}] d e n o t e g r e a t e s t i n t e g e r f u n c t i o n$ $t h e n v a l u e o f [{x e}^{- x}] = 0$ $s o g i v e n i n t r e g a l v a l u e i s z e r o$
	Commented by prof Abdo imad last updated on 16/Jun/18

	$h o w t o g e t t h i s r e s u l t s o r T a n m a y ?$
	Commented by tanmay.chaudhury50@gmail.com last updated on 16/Jun/18

	Commented by tanmay.chaudhury50@gmail.com last updated on 18/Jun/18

	$f r o m g r a p h a t t a c h e d i t i s c l e a r t h a t v a l u e o f$ ${x e}^{- x} < 1 s o [{x e}^{- x}] = 0 w h e n \infty > x ⩾ 0$
	Commented by abdo.msup.com last updated on 17/Jun/18

	$b u t x e^{- x} < 1 ⇏ [x e^{- x}] = 0$
	Commented by tanmay.chaudhury50@gmail.com last updated on 17/Jun/18

	$d o t h i s t h i r d b r a c k e t [{x e}^{- x}] i s g r e a t e s t i n t e g e r$ $o r f l o o r f u n c t i o n . . . i f y e s t h e n [{x e}^{- x}] = 0$ $o t h e r w i s e s o l v e i t . . .$
	Commented by tanmay.chaudhury50@gmail.com last updated on 17/Jun/18

	Commented by tanmay.chaudhury50@gmail.com last updated on 17/Jun/18

	Commented by tanmay.chaudhury50@gmail.com last updated on 17/Jun/18

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