搜搜考试网求定积分上限0 下限π/2 （e^-x）乘以sin2xdx
来源：学生作业帮 编辑：搜搜考试网作业帮 分类：数学作业 时间：2024/04/27 08:07:26
求定积分上限0 下限π/2 （e^-x）乘以sin2xdx
∫[π/2,0]e^-x * sin2x dx
= (-1/2)∫[π/2,0]e^-x dcos2x
= (1/2)∫[0,π/2]e^-x dcos2x
= (1/2)[e^-x * cos2x] - (1/2)∫[0,π/2]cos2x de^-x
= (1/2)[e^(-π/2) * (-1) - 1] + (1/4)(∫[0,π/2]e^-x dsin2x
= (1/2)[-e^(-π/2)-1] + (1/4)[e^-x * sin2x] + (1/4)∫[0,π/2]e^-x * sin2x dx
= (1/2)[-e^(-π/2)-1] - (1/4)∫[π/2,0]e^-x * sin2x dx
(1+1/4)∫[π/2,0]e^-x * sin2x dx = -(1/2)[e^(-π/2)+1]
∫[π/2,0]e^-x * sin2x dx = -(2/5)[e^(-π/2)+1]
= (-1/2)∫[π/2,0]e^-x dcos2x
= (1/2)∫[0,π/2]e^-x dcos2x
= (1/2)[e^-x * cos2x] - (1/2)∫[0,π/2]cos2x de^-x
= (1/2)[e^(-π/2) * (-1) - 1] + (1/4)(∫[0,π/2]e^-x dsin2x
= (1/2)[-e^(-π/2)-1] + (1/4)[e^-x * sin2x] + (1/4)∫[0,π/2]e^-x * sin2x dx
= (1/2)[-e^(-π/2)-1] - (1/4)∫[π/2,0]e^-x * sin2x dx
(1+1/4)∫[π/2,0]e^-x * sin2x dx = -(1/2)[e^(-π/2)+1]
∫[π/2,0]e^-x * sin2x dx = -(2/5)[e^(-π/2)+1]
求定积分x^4乘以根号下（1-x^2）,上限1,下限0
dx／（x乘以根号下（1+lnx））,上限e^2,下限1,求此定积分
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-
利用定义求定积分定积分号（积分下限0积分上限1）e^x dx
求SinX的平方乘以X定积分下限0上限π
求定积分∫（上限为e平方,下限为e）1/x乘以(lnx)平方dx
求定积分:(x乘以lnx)dx,上限是e,下限是1?
求定积分∫（ x^3)[e^(-x^2)] dx 上限(ln2)^1/2,下限0
求定积分（上限+∞下限0）e^(-根号下x）
求定积分∫上限1下限0 e^2x dx
求定积分∫上限ln2下限0 根号下（e^x-1）dx
求定积分 积分上限为1 下限为-1 ∫（1+x）乘以根号(1-x^2)