[（sin x-cos x）/(sin x+cos x)]^4 求定积分 积分区间0-π/4

来源：学生作业帮助网 编辑：作业帮 时间：2024/11/28 17:00:29
[（sin x-cos x）/(sin x+cos x)]^4 求定积分 积分区间0-π/4
xJ@_e@u:4˦}>@HEEb͂ek Z슟Hղ%Gw(+lfҲhxpΜ3dj2rK@Gлx1R2p_{~C6Zlz{?Eg ~>8P^w*C,}1.:g>SR#$-՝ -lLW9Vr^e[\vn)ѻƒq5\G~y(' fĀW`$ͳ,11.2Q ƁeDYt˝|Ը[h4 /AZ{t{Z3Qܗig.gvW~nuk}y/nb@p0dLLw !gJQuiw:<ު%cdCRNr>Sm;}8 @4w &Q_s!

[（sin x-cos x）/(sin x+cos x)]^4 求定积分 积分区间0-π/4
[（sin x-cos x）/(sin x+cos x)]^4 求定积分 积分区间0-π/4

[（sin x-cos x）/(sin x+cos x)]^4 求定积分 积分区间0-π/4
[（sin x-cos x）/(sin x+cos x)]^4 =[(1-tgx)/(1+tgx)]^4=[tg(x-45)}^4=[sec^2(x-45)-1]^2
由此再求,上面两答案都不对

∫[（sin x-cos x）/(sin x+cos x)]^4dx
=-∫(sin x+cos x)]^(-4)d(sin x+cos x)
=1/3*(sin x+cos x)^(-3)+c
积分区间0-π/4
=1/3*[(sin π/4+cosπ/4)^(-3)-(sin 0+cos0)^(-3)]
=1/3*(√2/4-1)
希望能帮到你...

全部展开

∫[（sin x-cos x）/(sin x+cos x)]^4dx
=-∫(sin x+cos x)]^(-4)d(sin x+cos x)
=1/3*(sin x+cos x)^(-3)+c
积分区间0-π/4
=1/3*[(sin π/4+cosπ/4)^(-3)-(sin 0+cos0)^(-3)]
=1/3*(√2/4-1)
希望能帮到你，祝学习进步O(∩_∩)O,也别忘了采纳！

收起

∫[0→π/4] [(sin x-cos x)/(sin x+cos x)]⁴dx
= ∫[0→π/4] d(-cos x-sin x)[1/(sin x+cos x)]⁴dx
= -∫[0→π/4] d(cos x+sin x)[1/(sin x+cos x)]⁴dx
= (1/3)∫[0→π/4] d[1/(sin x+cos x)]...

全部展开

∫[0→π/4] [(sin x-cos x)/(sin x+cos x)]⁴dx
= ∫[0→π/4] d(-cos x-sin x)[1/(sin x+cos x)]⁴dx
= -∫[0→π/4] d(cos x+sin x)[1/(sin x+cos x)]⁴dx
= (1/3)∫[0→π/4] d[1/(sin x+cos x)]³dx
= (1/3)[1/(sin x+cos x)]³ [0→π/4]
= [（根号2）/4 - 1]/3
= (根号2)/12 - 1/3

收起

sin（sin（sin（sin（x）=cos（cos（cos（cos（x）,X等于多少? sin（-x） cos(-x)等于多少 参数方程x=cos(sin+cos)y=sin（cos+sin）化为普通方程 cos x/sin x+sin x/(1+cos x) 化简. cos x /sin x= f（x）=sin x +cos x +sin x * cos x ,求值域 cos(-x)化简是-COS（X） SIN（-X）是SIN（X） cos(sin x)怎么解 已知tan=2,求(cos x+sin x)/(cos x-sin x)+sin^2x 化简(sin x+cos x-1)(sin x-cos x+1)/sin 2x 化简sin（2π+x）cos（π-x）sin（π-x）/cos（x-π）sin（-π-x）sin（π+x） 化简【完整步骤!】1.（sin^4x-sin^2x）/secx2.sin^4x-cos^4x【这道题的正确答案是sin^2x-cos^2x】 (x*sin x*cos x)的导数 请问sin（x+y）cos y-cos（x+y）sin y得多少 sin x/(sin x+cos x) 的不定积分 化简 cos^2(x)*sin^2(x)-sin^2(x) 化简sin^4x-sin^2x+cos^2x 化简:sin^4 x-sin^2 x+cos^2 x