prss.net
当前位置:首页 >> 证明定积分(0到π/2)sin^3x/(sinx+Cosx)Dx=定... >>

证明定积分(0到π/2)sin^3x/(sinx+Cosx)Dx=定...

解:∵(cosx)^4是偶函数,(sinx)^3是奇函数 ∴∫(cosx)^4dx=2∫(cosx)^4dx ∫(sinx)^3dx=0 故 ∫((cosx)^4+(sinx)^3)dx =∫(cosx)^4dx+∫(sinx)^3dx =2∫(cosx)^4 =(1/2)∫[3/2+2cos(2x)+cos(4x)/2]dx (应用倍角公式) =(1/2)[3x/2+sin(2x)+sin(4x)/8]│ =(1...

∫π/2 0 (cos2x/cosx+sinx)dx =∫π/2 0 (cos²x-sin²x)/(cosx+sinx)dx =∫π/2 0 (cosx-sinx)dx =sinx+cosx π/2 0 =(1+0)-(0+1) =0

lim(x→0)(sinx-xcosx)/(sin^3x) =lim(x→0)[(sinx-xcosx)]'/(sin^3x)' =lim(x→0)(cosx-cosx+xsinx)/[3(sin^2x)cosx] =lim(x-0) x/[3(sinxcosx)] =lim(x-0) x/[3sin(2x)/2] =lim(x-0) x'/[3sin(2x)/2]' =lim(x-0) 1/[3cos(2x)] =1/3

limx→0 (sinx-xcosx)/sin^3x =(1-xcotx)/sin²x =(tanx-x)/x³ 利用等价无穷小:sinx∽x∽tanx =(sec²x-1)/3x² 洛必达法则,上下求导 =tan²x/3x² =1/3 利用等价无穷小:x∽tanx

(sinx-cosx)(sin^2x+cos^2x+sinxcosx)=(sinx-cosx)(1+sinxcosx)=(sinx-cosx)(1+(sin2x)/2)=(sinx-cosx)(2+sin2x)/2 自己算了!~~

原式=sinx+cos(2x+x)=sinx+(1-2sinx平方)cosx+sin2x*sinx,因为sin2x=2sinxcosx,所以原式=sinx+cosx=根号2sin(x+π/4),周期就是2π

(x+sin(x))/(4cos(x)-4) 首先改写降次: xcos^4(x/2)/sin^3(x) = 1/8 xcot(x/2)csc^2(x/2) ... 注:csc(x)=1/sin(x) 换元积分:令u=x/2: dx=2du, ∫ 1/8 xcot(u)csc^2(u) 2du =1/8 * 2 * 2 ∫ ucot(u)csc^2(u) du 然后分部积分, =1/2 u(-1/2cot^2...

lim(x→0)(sinx-xcosx)/(sin^3x)=lim(x→0)[(sinx-xcosx)]'/(sin^3x)'=lim(x→0)(cosx-cosx+xsinx)/[3(sin^2x)cosx]=lim(x-0) x/[3(sinxcosx)]=lim(x-0) x/[3sin(2x)/2]=lim(x-0) x'/[3sin(2x)/2]'=lim(x-0) 1/[3cos(2x)]=1/3

网站首页 | 网站地图
All rights reserved Powered by www.prss.net
copyright ©right 2010-2021。
内容来自网络,如有侵犯请联系客服。zhit325@qq.com