计算二重积分I=∫∫0≤x≤π,0≤y≤πsin2xsin2ydxdy．
I=∫0πdx∫0πsin2xsin2ydy =(∫0πsin2xdx)2 ={∫0π[(1-cos2x)/2]dx}2， =[(1/2)x∣0π-1/4∫0πcos2xd(2x)]c =[π/2-(1/4)sin2x∣0π]2 =π2/4
计算二重积分I=∫∫0≤x≤π,0≤y≤πsin2xsin2ydxdy．
I=∫0πdx∫0πsin2xsin2ydy =(∫0πsin2xdx)2 ={∫0π[(1-cos2x)/2]dx}2， =[(1/2)x∣0π-1/4∫0πcos2xd(2x)]c =[π/2-(1/4)sin2x∣0π]2 =π2/4
