| 仭30572 / inTopicNo.3) |
丂Re[4]: f偑(a-1,b+1)傗(a,b)偱旝暘壜擻側傜佺[a to b]2f(x)f'(x)dx=(f(b))^2-(f(a))^2?
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仩搳峞幰/ miwa 堦斒恖(6夞)-(2008/01/07(Mon) 05:56:44)
 | 偛夞摎桳擄偆偛偞偄傑偡丅
> 婾側傜偽斀椺傪堦偮嶌偭偰嵍曈偲塃曈偺抣偑
> 堦抳偟側偄偙偲傪帵偣偽傛偄偲巚偄傑
> 偡丅
a=1,b=2偲偟丄f(x):=1/(x-1)(x-2)
側傞傕偺傪峫偊偰尒傞偲偙偺f(x)偼(a,b)偱旝暘壜擻偱
f'(x)=(-2x+3)/(x-1)^2(x-2)^2
偱
f'(x)=0偺帪,x=3/2
傛偭偰
f(x)偼x=3/2偱嬌戝抣-4傪偲傝x=1,x=2傪慟嬤慄偲偡傞嬋慄偲側傞丅
廬偭偰,
佺[1 to 2]2f(x)f'(x)dx=lim[(c,d)仺(1,2)]佺[c to d]2f(x)f'(x)dx
=lim[(c,d)仺(1,2)]佺[c to d]2f(x)f'(x)dx
=lim[(c,d)仺(1,2)]((f(d))^2-(f(c))^2)
=lim[(c,d)仺(1,2)](1/(d-1)^2(d-2)^2-1/(c-1)^2(c-2)^2)
偐傜愭偵恑傔傑偣傫丅
偙偙偐傜偳偆側傝傑偡偱偟傚偆偐?
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