zxpr.net
当前位置:首页 >> sin5xCos3x >>

sin5xCos3x

先积化和差,再积分! sin5xcos3x=0.5sin(8x)+0.5sin(2x) ∫sin5xcos3x dx =∫0.5sin(8x)+0.5sin(2x)dx =(1/16)∫sin(8x)d(8x) + (1/4)∫sin(2x)d(2x) =-(1/16)cos(8x) - (1/4)cos(2x) + C

y'=5cos5xcos3x-3sin5xsin3x y''=5(-5sin5xcos3x-3sin3xcos5x)-3(5cos5xsin3x+3cos3xsin5x) =-25sin5xcos3x-15sin3xcos5x-15sin3xcos5x-15sin5xcos3x =-40sin5xcos3x-30sin3xcos5x 没怎么算,不知对否。

sin3xcos5x=sin5xcos3x sin3xcos5x-sin5xcos3x=0 sin(3x-5x)=0 sin(-2x)=0 -sin2x=0 sin2x=0 x∈[0,4π] 2x=kπ;k∈Z x=kπ/2;k∈Z 所有解之和=π/2×(1+2+3+4+5+6+7+8)=(1+8)×8/2×(π/2)=18π

(cos5xcos3x)' =(-5sin5x)cos3x+(-3sin3x)cos5x =-5sin5xcos3x-3sin3xcos5x

 limsin3x/tan5x =lim3cos3x/[5(sec5x)^2] =(3/5)limcos3x(cos5x)^2 =(3/5)cos3π(cos5π)^2 =-3/5 limtanx/x=limx/x=1

如图

sin2xcos3x =1/2[sin(2x+3x)+sin(2x-3x)] =1/2(sin5x-sinx)

积化和差公式: sinαcosβ=1/2[sin(α+β)+sin(α-β)] 本题中,将3x看做α,2x看做β: sin3xcos2x = 1/2[sin(3x+2x)+sin(3x-2x)] = 1/2(sin5x+sinx)

使用积化和差公式一步到位 sinxcosy=(sin(x+y)+sin(x-y))/2

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