12 例2-2求由下列曲面围成的立体的体积 2)x2+y2+z2=2x,z=x2+y 〖解〗 FF. g1-ParametricPlot3DI(Sin u Cos vI, Sin uSin vI, Cosjul+1), {u,0,Pi/2},{v,0,2Pi g2-ParametricPlot3DRz"Cosv, z sin vl, z z,0, 1,v,0, 2Pill g3=ParametricPlot3DRz Cos vl," sin v,03, z0, 1,v,0, 2Pil ShowIgl, g2, g3, BoxRatios->(1, 1, 13, Shading->False, View Point- >3.350,-0.170,0.447 【注】区域为球顶锥底,选用球坐标较为简便4 丌丌/4 2 cosp I=Ja0∫ sinador'dr=z iAA: ntegrate[r/2*Sin[u], (v, 0, 2Pi),(u,0, Pi/4), (r,0, 2 Coslu)l=Pi2 2 2 2 2 (2) x + y + z = 2z, z = x + y 【注】区域为球顶锥底，选用球坐标较为简便 语句：ntegrate[r^2*Sin[u],{v,0,2Pi},{u,0,Pi/4},{r,0,2 Cos[u]}]=Pi g3=ParametricPlot3D[{z*Cos[v],z*Sin[v],0},{z,0,1},{v,0,2Pi}] g2=ParametricPlot3D[{z*Cos[v],z*Sin[v],z},{z,0,1},{v,0,2Pi}] Show[g1,g2,g3,BoxRatios->{1,1,1},Shading->False, ViewPoint- >{3.350,-0.170,0.447}] 程序 g1=ParametricPlot3D[{Sin[u]Cos[v],Sin[u]Sin[v],Cos[u]+1}, {u,0,Pi/2},{v,0,2Pi}] 例2-2 求由下列曲面围成的立体的体积 〖解〗 d d r dr    =       2 0 / 4 0 2cos 0 2 I sin = 