作者LuisSantos (^______^)
看板trans_math
标题Re: [积分] 几题积分
时间Tue Mar 6 00:58:11 2007
※ 引述《walolo (有缘无份)》之铭言：
: sin^2θ
: 1.∫ ----------- dθ
: cosθ
: cos2t
: 2.∫-----------dt
: sin^42t
: 3.∫θ√1-cosθ dθ
∫(θ)(√(1 - cosθ)) dθ
= ∫(θ)(√(1 - (1 - (2)((sin(θ/2))^2)))) dθ
= ∫(θ)(√((2)((sin(θ/2))^2))) dθ
= ∫(θ)(√2)(sin(θ/2)) dθ
= (√2)(∫(θ)(sin(θ/2)) dθ)
= (√2)((-2)(θ)(cos(θ/2)) - ∫(-2)(cos(θ/2)) dθ)
= (√2)((-2)(θ)(cos(θ/2)) - (-4)(sin(θ/2))) + c
= (√2)((-2θ)(cos(θ/2)) + (4)(sin(θ/2))) + c
= (-2)(√2)(θ)(cos(θ/2)) + (4√2)(sin(θ/2)) + c
: dx
: 4.∫-----------
: x√x^2－16
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