计算∬Dx2ycos(xy2)dxdy，D：0≤x≤π/2，0≤y≤2

计算∬_Dx²ycos(xy²)dxdy，D：0≤x≤π/2，0≤y≤2
【正确答案】：∬_Dx²ycos(xy²)dxdy=∫₀^π/2dx∫₀²x²ycos(xy²)dy =∫₀^π/2(1/2)x[sin(xy²)]|₀²dx=1/2∫₀^π/2xsin4xdx =1/2[(1/16)sin4x-(1/4xcos4x)]|₀^π/2=-(π/16)