Question

高数题求解

画问号的地方怎么来的呀

Answer 1

let
u=π/2-t
du=-dt
t=0, u=π/2
t=π/2 , u=0
I
=∫ (0->π/2) (sint)^2.cost/(sint+cost) dt
=∫ (π/2->0) [(cosu)^2.sinu/(sinu+cosu) ] (-du)
=∫ (0->π/2) [(cosu)^2.sinu/(sinu+cosu) ] du
=∫ (0->π/2) [(cost)^2.sint/(sint+cost) ] dt
2I
=∫ (0->π/2) (sint)^2.cost/(sint+cost) dt +∫ (0->π/2) [(cost)^2.sint/(sint+cost) ] dt
=∫ (0->π/2) sint.cost dt
=(1/2)∫ (0->π/2) sin2t dt
=-(1/4)[cos2t]|(0->π/2)
=(1/4)(1+1)
=1/2