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.

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