((sinx)^3-(sinx)^5)^1/2dx.定积分 上限派,下限0

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((sinx)^3-(sinx)^5)^1/2dx.定积分上限派,下限0((sinx)^3-(sinx)^5)^1/2dx.定积分上限派,下限0((sinx)^3-(sinx)^5)^1/2dx.定积

((sinx)^3-(sinx)^5)^1/2dx.定积分 上限派,下限0
((sinx)^3-(sinx)^5)^1/2dx.定积分 上限派,下限0

((sinx)^3-(sinx)^5)^1/2dx.定积分 上限派,下限0
∫(上限pi,下限0) [(sinx)^3-(sinx)^5]^(1/2) dx
=∫(上限pi,下限0) [(sinx)^3 *(1-(sinx)^2)]^(1/2) dx
=∫(上限pi,下限0) [(sinx)^3 *(cosx)^2]^(1/2) dx
=∫(上限pi/2,下限0) [(sinx)^3 *(cosx)^2]^(1/2) dx+∫(上限pi,下限pi/2) [(sinx)^3 *(cosx)^2]^(1/2)dx
=∫(上限pi/2,下限0) (sinx)^(3/2) *cosx dx-∫(上限pi,下限pi/2) (sinx)^(3/2) *cosx dx
=∫(上限pi/2,下限0) (sinx)^(3/2) dsinx-∫(上限pi,下限pi/2) (sinx)^(3/2) dsinx
=(2/5)(sinx)^(5/2) |(上限pi/2,下限0) -(2/5)(sinx)^(5/2) |(上限pi,下限pi/2)
=(2/5)+(2/5)
=4/5