ldcf.net
当前位置:首页 >> CosnxDx与sinnxDx在0到2派上的积分怎么算啊 >>

CosnxDx与sinnxDx在0到2派上的积分怎么算啊

几何法最简单,画个图,看面积,当然也可以用牛顿莱布尼茨公式,比较麻烦,但是是通用的

∫(3x^2+1)cosnxdx =(1/n)(3x^2+1)sinnx-(6/n)∫xsinnxdx =(1/n)(3x^2+1)sinnx+(6/n^2)xcosnx-(6/n^2)∫cosnxdx =(1/n)(3x^2+1)sinnx+(6/n^2)xcosnx-(6/n^3)sinnx+C 0到pai区间上的定积分 ={(1/n)(3π^2+1)sinnπ+(6/n^2)πcosnπ-(6/n^3)sinnπ} -{(1/n...

∫x^2cosnxdx =(1/n)∫x^2cosnxdnx =(1/n)∫x^2dsinnx =(1/n)x^2sinnx-(1/n)∫sinnxdx^2 =(1/n)x^2sinnx-(1/n)∫2xsinnxdx =(1/n)x^2sinnx-(2/n^2)∫xsinnxdnx =(1/n)x^2sinnx+(2/n^2)∫xdcosnx =(1/n)x^2sinnx+(2/n^2)xcosnx-(2/n^2)∫cosnxdx =(1/n)x^...

当n=0时, ∫ [-π/2-->0] x²dx =1/3x³ [-π/2-->0] =π³/24 当n>0时, ∫ [-π/2-->0] x²cosnx dx =(1/n)∫ [-π/2-->0] x² d(sinnx) =(1/n)x²sinnx-(1/n)∫ [-π/2-->0] 2xsinnx dx =(1/n)x²sinnx+(2/n²)∫ [-π/...

证明: ∫(2π,0) sinnx sinmxdx=,,, ∫(2π,0) cosnx cosmxdx=,,, ∫(2π,0) sinnx cosmxdx=,,, 当 m ≠ n 时, ∫(2π,0) sinnx sinmxdx= = (1/2) * ∫(2π,0) [ cos( m-n)x - cos( m+n)x ] dx = (1/2) * (2π,0) [ sin( m-n)x /(m-n) - sin( m+n...

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