作者LuisSantos (^______^)
看板trans_math
標題Re: [積分]
時間Thu Feb 15 03:25:07 2007
※ 引述《king911015 (早已放棄愛上你)》之銘言：
: 1.
: x + 4
: ∫---------------- dx =?
: x^3 + x^2 - 2
: 2.
: ∫ cos√x dx = ?
令 t = √x , 則 x = t^2 => dx = (2t) dt
∫ cos(√x) dx
= ∫ (cos(t))(2t) dt
= (2)(∫(t)(cos(t)) dt)
= (2)((t)(sin(t)) - ∫sin(t) dt)
(令 u = t , dv = cos(t) dt , 則 du = dt , v = sin(t) )
= (2)((t)(sin(t)) - (-cos(t))) + c
= (2)((t)(sin(t)) + (cos(t))) + c
= (2)(t)(sin(t)) + (2)(cos(t)) + c
= (2)(√x)(sin(√x)) + (2)(cos(√x)) + c
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