求曲面z=x2+2y2及曲面z=6-2x2-y2所围成的立体体积．
空间体在Oxy面上授影域为D：x2+y2≤2所求体积V为 V=∫∫D[(6-2x2-y2)-(x2+2y2)]dxdy =∫∫D[(6-3x2-3y2)dxdy =∫02πdθ∫0√2(6-3r2)rdr =6π
求曲面z=x2+2y2及曲面z=6-2x2-y2所围成的立体体积．
空间体在Oxy面上授影域为D：x2+y2≤2所求体积V为 V=∫∫D[(6-2x2-y2)-(x2+2y2)]dxdy =∫∫D[(6-3x2-3y2)dxdy =∫02πdθ∫0√2(6-3r2)rdr =6π
