Please Help...!! ∫^( ∞) _( 0) x.e^(−x) .sinx.dx


Question and Answers Forum

All Questions Topic List
Integration Questions
Previous in All Question Next in All Question
Previous in Integration Next in Integration
Question Number 193278 by Nimnim111118 last updated on 09/Jun/23

$P l e a s e H e l p . . .!!$ ${\int_{0}}^{\infty} x . e^{- x} . s i n x . d x$
	Answered by qaz last updated on 09/Jun/23
	$∫_0 ^∞ xe^(−x) sin xdx=−im∫_0 ^∞ xe^(−(1+i)x) dx =−im(1/((1+i)^2 ))=(1/2) −−−−− ∫_0 ^∞ xe^(−x) sin xdx=−DL{e^(−x) sin x}(s=0)=−D(1/((1+s)^2 +1))(s=0) =((2(1+s))/(((1+s)^2 +1)^2 ))(s=0)=(1/2)$
	$\int_{0}^{\infty} {x e}^{- x} \sin x d x = - i m \int_{0}^{\infty} {x e}^{- (1 + i) x} d x$ $= - i m \frac{1}{{(1 + i)}^{2}} = \frac{1}{2}$ $- - - - -$ $\int_{0}^{\infty} {x e}^{- x} \sin x d x = - D L {e^{- x} \sin x} (s = 0) = - D \frac{1}{{(1 + s)}^{2} + 1} (s = 0)$ $= \frac{2 (1 + s)}{{({(1 + s)}^{2} + 1)}^{2}} (s = 0) = \frac{1}{2}$
	Commented by Nimnim111118 last updated on 10/Jun/23

	$T h a n k y o u s i r .$ $B u t, I d o n t c l e a r l y u n d e r s t a n d i t .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum