为自己加油

∫∫_Dxy²cos(x²y)dσ，其中D={(x,y)∣0≤x≤2，0≤y≤π/2}．

∫∫_Dxy²cos(x²y)dσ=∫₀^π/2dy∫₀²xy²cos(x²y)dx =∫₀^π/2[(1/2)y∫₀²cos(x²y)d(x²y)]dy =1/2∫₀^π/2[ysin(x²y)∣₀²]dy =1/2∫₀^π/2ysin4ydy=-(1/8)∫₀^π/2ydcos4y =-(1/8)ycos4y∣₀^π/2+1/8∫₀^π/2cos4ydy =-(π/16)+(1/32)sin4y∣₀^π/2=-(π/16)