π --- 2 ∫ sin的3次方xcosxdx 0
作者&投稿:书菁 (若有异议请与网页底部的电邮联系)
进行凑微分即可
得到原积分
=∫sin²xd(sinx)
=1/3*sin³x
代入上下限2π和0
显然积分值为0
=∫[0,π/2] sin^3 xdsinx
=sin^4x/4[0,π/2]
=1/4
贡闵养胃: 可能会用到三倍角公式: sin3α = 3sinα-4sin³α = 4sinαsin(60°+α)sin(60°-α) cos3α = 4cos³α-3cosα = 4cosαcos(60°+α)cos(60°-α) tan3α = (3tanα-tan³α)/(1-3tan²α) = tanαtan(π/3+α)tan(π/3-α) 不过,这几个公式在高考中不常见,但还是应有所了解的.
长垣县13328329618: 化简:(1)、tan(2π+α)tan(π+α)cos( - π - α)的3次方分之sin( - α)的平方乘以cos(π+α); - ?
贡闵养胃: ⑴、原式=[(-sina)^2*(-cosa)]/[tana*tana*(-cosa)^3]=sin^2a/(tan^2a*cos^2a)=sin^2a/sin^2a=1;⑵、原式=[(-sina)*tana]/(-cosa)*[(-tana)]=-sina/cosa=-tana.
长垣县13328329618: 提问sinA的三次方在二分之π到二分之三π的积分是零还是三分之四啊 - ?
贡闵养胃: ∫[π/2,3π/2] (sinx)^3dx t=π-x x=π/2 t=π/2 x=3π/2 t=-π/2 =∫[π/2,-π/2](sin(π-t))^3d(π-t) =∫[-π/2,π/2](sint)^3 dt =0∫[-a,a](sint)^3dt=∫[-a,0](sint)^3dt +∫[0,a](sint)^3dt t=-u t=-a u=a t=0 u=0=∫[a,0](sin(-u)^3d(-u)+∫[0,a](sint)^3dt=∫[a,0](sinu)^3du+∫[0,a](sint)^3dt ...
长垣县13328329618: 已知sin(π - a) - cos(π+a)=(根号2)/3,(π/2<a<π) - ?
贡闵养胃: 1. sin(π-a)-cos(π+a)=sina+cosa=√2/3 平方 1+2sinacosa=2/9 2sinacosa=-7/9 π/20 cosa0( sina-cosa)^2=1-2sinacosa=1+7/9=16/9 sina-cosa=4/32. sin的三次方(2π-a)+cos的三次方(2π-a)=sin^2a+cos^2a=(sina+cosa)(sin^2a-sinacosa+cos^2a)=√2/3*(1+7/18) =25√2/54
长垣县13328329618: a∈(0,π/2) 则sin三次方a/cosa+cos三次方a/sina最小值 - ?
贡闵养胃: 解答:a∈(0,π/2) sina*cosa=(1/2)sin2a∈(0,1/2] 则0<sina<1,0<cosa<1 ∴ sin三次方a/cosa+cos三次方a/sina =[(sina)^4]+(cosa)^4]/(sinacosa) = [(sin²a+cos²a)²-2sin²cos²a]/(sinacosa) =(1-2sin²acos²a)/sinacosa =1/(sinacosa)-2sinacosa 换元,令t=sinacosa =1/t-2t 在(0,1/2]上是减函数和 ∴ t=1/2时,原式有最小值1/(1/2)-2*(1/2)=1 即sin三次方a/cosa+cos三次方a/sina最小值为1
长垣县13328329618: 已知sin(3π+θ)=lg1/(10开3次方) 求{cos(π+θ)/cosθ[cos(π - θ) - 1]}+{ cos(θ - 2π)/sin(θ - 3π/2 - ?
贡闵养胃: sin(3π+θ)=lg1/10^(1/3)=lg10^(-1/3)=-1/3 sin(3π+θ)=sin(π+θ)=-sinθ 所以sinθ=1/3 原式=[-cosθ/[cosθ(-cosθ-1)]+[cosθ/cosθ(-cosθ)+cosθ]=1/(1+cosθ)+1/(1-cosθ)=(1-cosθ+1+cosθ)/sin²θ=2/(1/3)²=18
长垣县13328329618: ∫[0_->π/2]cosθsin³θdθ 详细求解!!!急急急 !!!!!!!!!! - ?
贡闵养胃: ∫[0-->π/2]cosθsin³θdθ =∫sin³θdsinθ=1/4(sinθ)^4|[0-->π/2]=1/4
长垣县13328329618: 定积分 ∫2分之π 0 (sinx+e的 - 2x次方)dx - ?
贡闵养胃: =∫[0,π/2]sinxdx+∫[0,π/2]e^(-2x)dx=1+1/2(1-e^(-π))=(3-e^(-π))/2
长垣县13328329618: 求正弦,余弦函数N次方不定积分公式,注意是N次方啊.我们老师介绍过公式的不过我忘记了,即∫sin^n=?,∫cos^n=? - ?
贡闵养胃:[答案] In=∫(0,π/2)[cos(x)]^ndx=∫(0,π/2)[sin(x)]^ndx =(n-1)/n*(n-3)/(n-2)*…*4/5*2/3,n为奇数; =(n-1)/n*(n-3)/(n-2)*…*3/4*1/2*π/2,n为偶数
长垣县13328329618: πr的三次方减πr的二次方= - ?
贡闵养胃: πr的三次方减πr的二次方 =πr的二次方(r-1)