原式=1/2∫(0,π/2)ydy∫(0,2)cos(x²y)d(x²y)
=1/2∫(0,π/2)ysin(4y)dy
=1/2[-π/8+1/4∫(0,π/2)cos(4y)dy] (应用分部积分法)
=1/2(-π/8)
=-π/16.