Question

高数，定积分，请问图中红色框的步骤是怎么来的？

Answer 1

let
u=π-x
du=-dx
x=0, u=π
x=π,u=0
I
=∫(0->π) x|sinx| dx
=∫(0->π) x.sinx dx
=∫(π->0) (π-u).sinu (-du)
=∫(0->π) (π-u).sinu du
=∫(0->π) (π-x).sinx dx
2∫(0->π) x.sinx dx =π∫(0->π) sinx dx
∫(0->π) x.sinx dx =(π/2)∫(0->π) sinx dx

Answer 2

简单计算一下即可，答案如图所示