∫(sinx)^2/[1+e^(-x)] dx 积分上下限(π/4,π/4)怎么算?
来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/09/22 14:24:04
∫(sinx)^2/[1+e^(-x)] dx 积分上下限(π/4,π/4)怎么算?
注:此题的上下限有错,应该是积分上下限(-π/4,π/4)!
原式=∫(-π/4,π/4)(sinx)^2/[1+e^(-x)]dx (∫(-π/4,π/4)表示从-π/4到π/4积分)
=∫(-π/4,0)(sinx)^2/[1+e^(-x)]dx+∫(0,π/4)(sinx)^2/[1+e^(-x)]dx
=-∫(π/4,0)(sinx)^2/(1+e^x)dx+∫(0,π/4)(sinx)^2/[1+e^(-x)]dx (第一个积分用-x代换x得)
=∫(0,π/4)(sinx)^2/(1+e^x)dx+∫(0,π/4)e^x(sinx)^2/(1+e^x)dx (第二个积分分子分母同乘e^x得)
=∫(0,π/4)(1+e^x)(sinx)^2/(1+e^x)dx
=∫(0,π/4)(sinx)^2dx
=1/2∫(0,π/4)[1-cos(2x)]dx ()
=1/2[x-1/2sin(2x)]|(0,π/4)
=1/2(π/4-1/2)
=(π-2)/8
原式=∫(-π/4,π/4)(sinx)^2/[1+e^(-x)]dx (∫(-π/4,π/4)表示从-π/4到π/4积分)
=∫(-π/4,0)(sinx)^2/[1+e^(-x)]dx+∫(0,π/4)(sinx)^2/[1+e^(-x)]dx
=-∫(π/4,0)(sinx)^2/(1+e^x)dx+∫(0,π/4)(sinx)^2/[1+e^(-x)]dx (第一个积分用-x代换x得)
=∫(0,π/4)(sinx)^2/(1+e^x)dx+∫(0,π/4)e^x(sinx)^2/(1+e^x)dx (第二个积分分子分母同乘e^x得)
=∫(0,π/4)(1+e^x)(sinx)^2/(1+e^x)dx
=∫(0,π/4)(sinx)^2dx
=1/2∫(0,π/4)[1-cos(2x)]dx ()
=1/2[x-1/2sin(2x)]|(0,π/4)
=1/2(π/4-1/2)
=(π-2)/8
∫(sinx)^2/[1+e^(-x)] dx 积分上下限(π/4,π/4)怎么算?
∫sinx/(1+e^(-x))dx 定积分 下限是-π/4,上限是π/4
∫sin2x/[4+e^(sinx)^2]dx=?积分上限π/2,下限0
定积分∫下限(-π/4) 上限(π/4)(x/(1+sinx))dx
∫积分上限1积分下限-1 (2+sinx)/根号(4-x^2)dx
积分x/(sinx)^2上限π/3,下限π/4 定积分e^x/2 / 根号下1+e^(-x)上限1,下限0 定积分(1-
求解定积分∫e^(ax) cos(4x) dx 积分上下限为0到 π
大学文科数学定积分请问这题怎么做?∫[(sinx)^2009(cosx)^2010+x^2]dx积分上下限为π和-π看不
求定积分?∫ 1/(√1-x*x)dx,上限1/2,下限-1/2?arc sinx 如果将上下限代入,要怎么计算?
求定积分上限 1下限-1 sinx/(1+x^2+x^4)dx
利用函数的奇偶性计算此积分 ∫上限π,下限-π x^2*sinx dx
求一道定积分 ∫x/(1+sinx) dx 上限pi/4 下限-pi/4