计算二重积分I=∫∫_{0≤x≤π,0≤y≤π}sin²xsin²ydxdy．

计算二重积分I=∫∫_{0≤x≤π,0≤y≤π}sin²xsin²ydxdy．

I=∫₀^πdx∫₀^πsin²xsin²ydy =(∫₀^πsin²xdx)² ={∫₀^π[(1-cos2x)/2]dx}²， =[(1/2)x∣₀^π-1/4∫₀^πcos2xd(2x)]c =[π/2-(1/4)sin2x∣₀^π]² =π²/4