∫∫(D)e^(x/y)dxdy=∫(0,1)dy∫(y²,y)e^(x/y)dx (∫(0,1)表示从0到1积分,其它类同)
=∫(0,1)dy∫(y²,y)ye^(x/y)d(x/y)
=∫(0,1){[ye^(x/y)]│(y²,y)}dy
=∫(0,1)y(e-e^y)dy
=e∫(0,1)ydy-∫(0,1)ye^ydy
=(ey²/2)│(0,1)-(ye^y)│(0,1)+∫(0,1)e^ydy (应用分部积分法)
=e/2-e+(e^y)│(0,1)
=-e/2+e-1
=e/2-1.