设D是Oxy平面上x=0，Y=0和a+y=1所围区域，求以D为底，曲面z=x2+y2为顶的曲顶柱体的体积．
V=∫∫D(x2+y2)dxdy =∫01dx∫01-x(x2+y2)dy= ∫01[x2y+(1/3)y3)∣01-xdx =∫01x2(1-x)dx+(1/3)∫01(1-x)3dx =[(1/3)x3∣01]-[(1/4)x4∣01]-1/12 (1-x)4∣01=1/6
设D是Oxy平面上x=0，Y=0和a+y=1所围区域，求以D为底，曲面z=x2+y2为顶的曲顶柱体的体积．
V=∫∫D(x2+y2)dxdy =∫01dx∫01-x(x2+y2)dy= ∫01[x2y+(1/3)y3)∣01-xdx =∫01x2(1-x)dx+(1/3)∫01(1-x)3dx =[(1/3)x3∣01]-[(1/4)x4∣01]-1/12 (1-x)4∣01=1/6
