设secx=√2sint
则当x=0时,t=π/4
当x=π/4时,t=π/2
且d(secx)=√2costdt
于是,原式=∫(π/4,π/2)2cos²tdt
=∫(π/4,π/2)[1+cos(2t)]dt
=[t+sin(2t)/2]│(π/4,π/2)
=π/2-π/4-1/2.