Question

急急急，，这道题怎么写

在线等

Answer 1

令定积分为A
A=∫(π.0)(π-u)sin(π-u)/(1+cos²(π-u))d(π-u)
=∫(0.π)(π-u)sinu/(1+cos²u)du
=(1/2)∫πsinu/(1+cos²u)du
=-π/2∫1/(1+cos²u)dcosu
=(-π/2)arctan(cosu)
=π²/4