Question

定积分上限的π是怎么变到π/2的？

如图，第一个等号我能看明白，但是第二个等号这里的积分上限是怎么从π变成了π/2的？

Answer 1

令a=π即可，详情如图所示

Answer 2

如图所示：

Answer 3

let
u=π-x
du=-dx
x=π/2, u=π/2
x=π , u=0
∫(0->π) √[(sinx)^2-(sinx)^4 ] dx
=∫(0->π/2) √[(sinx)^2-(sinx)^4 ] dx +∫(π/2->π) √[(sinx)^2-(sinx)^4 ] dx
=∫(0->π/2) √[(sinx)^2-(sinx)^4 ] dx +∫(π/2->0) √[(sinu)^2-(sinu)^4 ] (-du)
=∫(0->π/2) √[(sinx)^2-(sinx)^4 ] dx +∫(0->π/2) √[(sinu)^2-(sinu)^4 ] du
=∫(0->π/2) √[(sinx)^2-(sinx)^4 ] dx +∫(0->π/2) √[(sinx)^2-(sinx)^4 ] dx
=2∫(0->π/2) √[(sinx)^2-(sinx)^4 ] dx