不定积分,(sin x+x^2)/(xcosx)^2.上限是派/4.下限是-派/4.
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/14 06:05:36
![不定积分,(sin x+x^2)/(xcosx)^2.上限是派/4.下限是-派/4.](/uploads/image/z/10370495-47-5.jpg?t=%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%2C%EF%BC%88sin+x%2Bx%5E2%EF%BC%89%2F%28xcosx%29%5E2.%E4%B8%8A%E9%99%90%E6%98%AF%E6%B4%BE%2F4.%E4%B8%8B%E9%99%90%E6%98%AF%EF%BC%8D%E6%B4%BE%2F4.)
x){YϗѦ~OGqfBvE=qFzOvt9ٌ϶7r!{z!"6IE3LΆn{7~G5t7M0ԊKS*T@$ЕMUrMCd={iF&O?ml3u5A)H.x>e]}"d"d>P4@I(I̫DWAVPWCCF 1\ A
-
不定积分,(sin x+x^2)/(xcosx)^2.上限是派/4.下限是-派/4.
不定积分,(sin x+x^2)/(xcosx)^2.上限是派/4.下限是-派/4.
不定积分,(sin x+x^2)/(xcosx)^2.上限是派/4.下限是-派/4.
原式=∫(-π/4,π/4)sinx/(xcosx)²dx+∫(-π/4,π/4)x²/(xcosx)²dx
=∫(-π/4,π/4)sinx/(xcosx)²dx+∫(-π/4,π/4)dx/cos²x
∵若f(x)是奇函数,则∫(-a,a)f(x)de=0
由于sinx/(xcosx)²是奇函数
∴∫(-π/4,π/4)sinx/(xcosx)²dx=0
∴原式=0+∫(-π/4,π/4)dx/cos²x
=∫(-π/4,π/4)d(tanx)
=(tanx)|(-π/4,π/4)
=1-(-1)
=2