定积分上限π\/2下限0sin^6x\/(sin^6x+cos^6x)dx
令x=π\/2-t,原积分=∫(0,π\/2)cos^6t\/sin^6t+cos^6tdt,这两个积分相加得π\/2,所以原积分=π\/4
sinx的6次方在0到π的范围内的定积分怎么算?求过程!
解法1：∫sin^6xdx =-(1\/6)sin^5xcosx-(5\/24)sin^3x-(5\/16)cosxsinx+5\/16x 将π和0分别代入上式相减得：=5π\/16-0=5π\/16 解法2：
(sin^6x+cos^5x)dx在区间0到π\/2之间的定积分
11\/30 凑微分
sin^6x+cos^6x的高n阶导数
利用立方和公式sin^6x+cos^6x=(sin^2x+cos^2x)(sin^4x+cos^4x-sin^2xcos^2x)=sin^4x+cos^4x-sin^2xcos^2x=(sin^2x+cos^2x)^2-3sin^2xcos^2x=1-3sin^2xcos^2x=1-3\/4·(sin4x)^2=5\/8+3\/8·cos8x所以,n阶导数为3\/8·8^n...
求不定积分∫sin^3x\/cos^6xdx
简单分析一下，详情如图所示
(sin2x\/(sin ^6x+cos^6 x))dx的不定积分
∫dx\/(sin^6x+cos^6x)＝∫[1+(tanx)^2]^2d(tanx)\/[1＋(tanx)^6] 令t＝tanx＝∫[1+2t^2＋t^4]dt\/[1＋t^6]＝∫[1－t^2＋t^4＋3t^2]dt\/[1＋t^6]＝∫dt\/[1＋t^2]＋∫[3t^2]dt\/[1＋t^6]＝arctant＋arctan(t^3)＋C＝x＋arc...
大一!!!高数!!!悬赏一百,求解一个定积分!!!谢谢大神!!!
根据公式：∫(0,π)xf(sinx)dx =π\/2∫(0,π)f(sinx)dx 可得 原式 =π\/2 ∫(0,π)sin^6xcos^4xdx =π∫(0,π\/2)sin^6x[1-sin^2x]^2dx =π∫(0,π\/2)sin^6x[1-2sin^2x+sin^4x]dx =π∫(0,π\/2)[sin^6x-2sin^8x+sin^10x]dx =π×【5\/6×3\/4×1\/2×π\/...
sin^6x+cos^6x怎么降幂,急
sin^6x+cos^6x 用立方和公式 =(sin^2x+cos^2x)(sin^4x -sin^2xcos^2x + cos^4x)=(sin^2x+cos^2x)^2-3sin^2xcos^2x =1-(3\/4)sin^2(2x) 还可以降次到cos4x =5\/8+(3\/8)cos4x
sin^6x+cos^6x怎么降幂,急
sin^6x+cos^6x 用立方和公式 =(sin^2x+cos^2x)(sin^4x -sin^2xcos^2x + cos^4x)=(sin^2x+cos^2x)^2-3sin^2xcos^2x =1-(3\/4)sin^2(2x) 还可以降次到cos4x =5\/8+(3\/8)cos4x
cos^6X在(0,2pai)上的定积分??求助高数高手。即cosx的6次方在(0,2pa...
∵cos^6x周期为π ∫[0，2π] cos^6x dx = 2∫[0，π] cos^6x dx = 2I 令x=π\/2-y => y=π\/2-x，dy=-dx 当x=0，y=π\/2 \/\/ 当x=π，y=-π\/2 I = -∫[π\/2，-π\/2] cos^6(π\/2-y) dy = ∫[-π\/2，π\/2] sin^6y dy = 2∫[0，π\/2] sin^6y dy...
