计算下列积分∫上限是2下限是1(根号下(x^2-1)dx/x)
来源:学生作业帮 编辑:大师作文网作业帮 分类:数学作业 时间:2024/10/05 15:35:45
计算下列积分∫上限是2下限是1(根号下(x^2-1)dx/x)
令x = secz,dx = secztanz dz
x > 1,z ∈[0,π/2),√(x² - 1) = √(sec²z - 1) = tanz
∫(1~2) √(x² - 1)/x dx
= ∫(0~π/3) tanz/secz * secztanz dz
= ∫(0~π/3) tan²z dz
= ∫(0~π/3) (sec²z - 1) dz
= [tanz - z] |(0~π/3)
= [tan(π/3) - π/3] - [tan(0) - 0]
= √3 - π/3
x > 1,z ∈[0,π/2),√(x² - 1) = √(sec²z - 1) = tanz
∫(1~2) √(x² - 1)/x dx
= ∫(0~π/3) tanz/secz * secztanz dz
= ∫(0~π/3) tan²z dz
= ∫(0~π/3) (sec²z - 1) dz
= [tanz - z] |(0~π/3)
= [tan(π/3) - π/3] - [tan(0) - 0]
= √3 - π/3
计算下列积分∫上限是2下限是1(根号下(x^2-1)dx/x)
.∫根号下(1+x)dx上限是1,下限是0,计算定积分
求定积分:[(2+根号下x)分之1]dx,上限是1,下限是0?
计算反常积分∫1/(x+2)(x+3)dx 上限是+∞ 下限是0
积分上限2,积分下限0,dx/根号下x+1+根号下(X+1)^3
计算定积分 ∫(x+3)/根号(2x+1)dx,上限4,下限0
求积分∫上限1下限-1ln(x+根号下1+x^2)dx
求(根号x+1/x)dx的定积分,上限是2,下限是1
计算积分 ∫(上限1,下限0)dx∫(上限1,下限x)siny^2dy
判断瑕积分的敛散性 ∫1/(3次根号下(x^2*(1-x))) dx 积分上限是1 下限是0
求定积分∫上限2,下限1 dx / (根号下4-x^2),
求定积分:arctan(根号下x)dx,上限是1,下限是0?