已知平行截面面积求立体的体积：图形、动画、计算

nullnull已知平行截面的面积求体积 （切片法）蜀南竹海null用数学软件Maple作了有关动画 这些动画生动地显示了立体的形成过程 计算了一些立体的体积nullnullwith(plots): f:=x->x^2/10+1: g:=x->-x^4/150-1: a:=-3:b:=3:H:=3: xzou:=spacecurve([x,0,0],x=a-1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=a-1..b+1,thickness=3,color=black): base:=plot3d([x,y,0],x=a..b,y=g(x)..f(x),color=grey,style=patchnogrid): quxianf:=spacecurve([x,f(x),0],x=a-1..b+1,thickness=3,color=red): quxiang:=spacecurve([x,g(x),0],x=a-1..b+1,thickness=3,color=red): K:=50:for i from 0 to K do xi:=a+i*(b-a)/K: sanjiaoxing[i]:=spacecurve([[xi,g(xi),0],[xi,f(xi),0],[xi,(f(xi)+g(xi))/2,H],[xi,g(xi),0]],thickness=3,color=blue): sanjiaoban[i]:=plot3d([xi,y,z],y=(f(xi)+g(xi))/2-(f(xi)-g(xi))/2*(1-z/H)..(f(xi)+g(xi))/2+(f(xi)-g(xi))/2*(1-z/H),z=0..H,color=yellow,style=patchnogrid): qumian1[i]:=plot3d([x,f(x)+(-f(x)+g(x))/2*t,H*t],t=0..1,x=a..xi,color=green): qumian2[i]:=plot3d([x,g(x)+(f(x)-g(x))/2*t,H*t],t=0..1,x=a..xi,color=green)od: sanjiaoxing:=display(seq(sanjiaoxing[i],i=0..K),insequence=true): sanjiaoban:=display(seq(sanjiaoban[i],i=0..K),insequence=true): qumian1:=display(seq(qumian1[i],i=0..K),insequence=true): qumian2:=display(seq(qumian2[i],i=0..K),insequence=true): display(xzou,yzou,base,quxianf,quxiang,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained);动画的Maple程序nullf:=x->(3/2)*(x^2/10+x^4/150+2): a:=-3:b:=3: Integrate(f(x),x=a..b)=integrate(f(x),x=a..b);现在来求这个立体的体积null这个立体叫做正劈锥体nullwith(plots): R:=1: f:=x->sqrt(R^2-x^2): g:=x->-sqrt(R^2-x^2): a:=-R:b:=R:H:=2: xzou:=spacecurve([x,0,0],x=a-1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=a-1..b+1,thickness=3,color=black): base:=plot3d([x,y,0],x=a..b,y=g(x)..f(x),color=grey,style=patchnogrid): quxian:=spacecurve([R*cos(t),R*sin(t),0],t=0..2*Pi,thickness=3,color=red): K:=60:for i from 0 to K do xi:=a+i*(b-a)/K: sanjiaoxing[i]:=spacecurve([[xi,g(xi),0],[xi,f(xi),0],[xi,(f(xi)+g(xi))/2,H],[xi,g(xi),0]],thickness=3,color=blue): sanjiaoban[i]:=plot3d([xi,y,z],y=(f(xi)+g(xi))/2-(f(xi)-g(xi))/2*(1-z/H)..(f(xi)+g(xi))/2+(f(xi)-g(xi))/2*(1-z/H),z=0..H,color=yellow,style=patchnogrid): qumian1[i]:=plot3d([x,f(x)+(-f(x)+g(x))/2*t,H*t],t=0..1,x=a..xi,color=green): qumian2[i]:=plot3d([x,g(x)+(f(x)-g(x))/2*t,H*t],t=0..1,x=a..xi,color=green)od: sanjiaoxing:=display(seq(sanjiaoxing[i],i=0..K),insequence=true): sanjiaoban:=display(seq(sanjiaoban[i],i=0..K),insequence=true): qumian1:=display(seq(qumian1[i],i=0..K),insequence=true): qumian2:=display(seq(qumian2[i],i=0..K),insequence=true): display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained,orientation=[-50,70]);动画的Maple程序nullwith(plots): R:=1: f:=x->sqrt(R^2-x^2): g:=x->-sqrt(R^2-x^2): a:=-R:b:=R:H:=2: xzou:=spacecurve([x,0,0],x=a-1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=a-1..b+1,thickness=3,color=black): base:=plot3d([x,y,0],x=a..b,y=g(x)..f(x),color=grey,style=patchnogrid): quxian:=spacecurve([R*cos(t),R*sin(t),0],t=0..2*Pi,thickness=3,color=red): xi:=0.5*R: sanjiaoxing:=spacecurve([[xi,g(xi),0],[xi,f(xi),0],[xi,(f(xi)+g(xi))/2,H],[xi,g(xi),0]],thickness=3,color=blue): sanjiaoban:=plot3d([xi,y,z],y=(f(xi)+g(xi))/2-(f(xi)-g(xi))/2*(1-z/H)..(f(xi)+g(xi))/2+(f(xi)-g(xi))/2*(1-z/H),z=0..H,color=yellow,style=patchnogrid): qumian1:=plot3d([x,f(x)+(-f(x)+g(x))/2*t,H*t],t=0..1,x=a..xi,color=green): qumian2:=plot3d([x,g(x)+(f(x)-g(x))/2*t,H*t],t=0..1,x=a..xi,color=green): display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained,orientation=[-50,70]);nullwith(plots): R:=1.7: f:=x->sqrt(R^2-x^2): g:=x->-sqrt(R^2-x^2): a:=-R:b:=R:H:=3: xzou:=spacecurve([x,0,0],x=a-1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=a-1..b+1,thickness=3,color=black): base:=plot3d([x,y,0],x=a..b,y=g(x)..f(x),color=grey,style=patchnogrid): quxian:=spacecurve([R*cos(t),R*sin(t),0],t=0..2*Pi,thickness=3,color=red): K:=8:for i from 0 to K do xi:=a+i*(b-a)/K: sanjiaoxing[i]:=spacecurve([[xi,g(xi),0],[xi,f(xi),0],[xi,(f(xi)+g(xi))/2,H],[xi,g(xi),0]],thickness=3,color=blue): sanjiaoban[i]:=plot3d([xi,y,z],y=(f(xi)+g(xi))/2-(f(xi)-g(xi))/2*(1-z/H)..(f(xi)+g(xi))/2+(f(xi)-g(xi))/2*(1-z/H),z=0..H,color=yellow,style=patchnogrid): od: sanjiaoxing:=display(seq(sanjiaoxing[i],i=0..K),insequence=false): sanjiaoban:=display(seq(sanjiaoban[i],i=0..K),insequence=false): qumian1:=plot3d([x,f(x)+(-f(x)+g(x))/2*t,H*t],t=0..1,x=a..b,color=green,style=wireframe,grid=[50,30]): qumian2:=plot3d([x,g(x)+(f(x)-g(x))/2*t,H*t],t=0..1,x=a..b,color=green,style=wireframe,grid=[50,30]): display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained,orientation=[-50,70]);null见同济《高等数学》6版，281页，例10现在来求这个立体的体积nullnullwith(plots): f:=x->sin(x/2)+2: g:=x->cos(x/3)-2: a:=-Pi:b:=Pi: xzou:=spacecurve([x,0,0],x=a-1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=a-1..b+1,thickness=3,color=black): base:=plot3d([x,y,0],x=a..b,y=g(x)..f(x),color=grey,style=patchnogrid): quxianf:=spacecurve([x,f(x),0],x=a-1..b+1,thickness=3,color=red): quxiang:=spacecurve([x,g(x),0],x=a-1..b+1,thickness=3,color=red): K:=60:for i from 0 to K do xi:=a+i*(b-a)/K: sanjiaoxing[i]:=spacecurve([[xi,g(xi),0],[xi,f(xi),0],[xi,(f(xi)+g(xi))/2,sqrt(3)/2*(f(xi)-g(xi))],[xi,g(xi),0]],thickness=3,color=blue): sanjiaoban[i]:=plot3d([xi,y,z],y=(f(xi)+g(xi))/2-(f(xi)-g(xi))/2+z/sqrt(3)..(f(xi)+g(xi))/2+(f(xi)-g(xi))/2-z/sqrt(3),z=0..sqrt(3)/2*(f(xi)-g(xi)),color=yellow,style=patchnogrid): qumian1[i]:=plot3d([x,f(x)+(-f(x)+g(x))/2*t,(sqrt(3)/2)*(f(x)-g(x))*t],t=0..1,x=a..xi,color=green): qumian2[i]:=plot3d([x,g(x)+(f(x)-g(x))/2*t,(sqrt(3)/2)*(f(x)-g(x))*t],t=0..1,x=a..xi,color=green)od: sanjiaoxing:=display(seq(sanjiaoxing[i],i=0..K),insequence=true): sanjiaoban:=display(seq(sanjiaoban[i],i=0..K),insequence=true): qumian1:=display(seq(qumian1[i],i=0..K),insequence=true): qumian2:=display(seq(qumian2[i],i=0..K),insequence=true): display(xzou,yzou,base,quxianf,quxiang,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained);动画的Maple程序nullf:=x->(sqrt(3)/4)*(sin(x/2)-cos(x/3)+4)^2: a:=-Pi:b:=Pi: Integrate(f(x),x=a..b)=integrate(f(x),x=a..b); evalf(%);现在来求这个立体的体积nullnullR:=1.6: f:=x->sqrt(R^2-x^2): g:=x->-sqrt(R^2-x^2): a:=-R:b:=R:H:=2: xzou:=spacecurve([x,0,0],x=a-1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=a-1..b+1,thickness=3,color=black): base:=plot3d([x,y,0],x=a..b,y=g(x)..f(x),color=grey,style=patchnogrid): quxian:=spacecurve([R*cos(t),R*sin(t),0],t=0..2*Pi,thickness=3,color=red): K:=60:for i from 0 to K do xi:=a+i*(b-a)/K: sanjiaoxing[i]:=spacecurve([[xi,g(xi),0],[xi,f(xi),0],[xi,(f(xi)+g(xi))/2,sqrt(3)/2*(f(xi)-g(xi))],[xi,g(xi),0]],thickness=3,color=blue): sanjiaoban[i]:=plot3d([xi,y,z],y=(f(xi)+g(xi))/2-(f(xi)-g(xi))/2+z/sqrt(3)..(f(xi)+g(xi))/2+(f(xi)-g(xi))/2-z/sqrt(3),z=0..sqrt(3)/2*(f(xi)-g(xi)),color=yellow,style=patchnogrid): qumian1[i]:=plot3d([x,f(x)+(-f(x)+g(x))/2*t,(sqrt(3)/2)*(f(x)-g(x))*t],t=0..1,x=a..xi,color=green): qumian2[i]:=plot3d([x,g(x)+(f(x)-g(x))/2*t,(sqrt(3)/2)*(f(x)-g(x))*t],t=0..1,x=a..xi,color=green)od: sanjiaoxing:=display(seq(sanjiaoxing[i],i=0..K),insequence=true): sanjiaoban:=display(seq(sanjiaoban[i],i=0..K),insequence=true): qumian1:=display(seq(qumian1[i],i=0..K),insequence=true): qumian2:=display(seq(qumian2[i],i=0..K),insequence=true): display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained,orientation=[-50,70]);动画的Maple程序nullR:=1.6: f:=x->sqrt(R^2-x^2): g:=x->-sqrt(R^2-x^2): a:=-R:b:=R:H:=2: xzou:=spacecurve([x,0,0],x=a-1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=a-1..b+1,thickness=3,color=black): base:=plot3d([x,y,0],x=a..b,y=g(x)..f(x),color=grey,style=patchnogrid): quxian:=spacecurve([R*cos(t),R*sin(t),0],t=0..2*Pi,thickness=3,color=red): xi:=0.2*R: sanjiaoxing:=spacecurve([[xi,g(xi),0],[xi,f(xi),0],[xi,(f(xi)+g(xi))/2,sqrt(3)/2*(f(xi)-g(xi))],[xi,g(xi),0]],thickness=3,color=blue): sanjiaoban:=plot3d([xi,y,z],y=(f(xi)+g(xi))/2-(f(xi)-g(xi))/2+z/sqrt(3)..(f(xi)+g(xi))/2+(f(xi)-g(xi))/2-z/sqrt(3),z=0..sqrt(3)/2*(f(xi)-g(xi)),color=yellow,style=patchnogrid): qumian1:=plot3d([x,f(x)+(-f(x)+g(x))/2*t,(sqrt(3)/2)*(f(x)-g(x))*t],t=0..1,x=a..xi,color=green): qumian2:=plot3d([x,g(x)+(f(x)-g(x))/2*t,(sqrt(3)/2)*(f(x)-g(x))*t],t=0..1,x=a..xi,color=green): display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained,orientation=[-50,70]); nullR:=1.6: f:=x->sqrt(R^2-x^2): g:=x->-sqrt(R^2-x^2): a:=-R:b:=R:H:=2: xzou:=spacecurve([x,0,0],x=a-1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=a-1..b+1,thickness=3,color=black): base:=plot3d([x,y,0],x=a..b,y=g(x)..f(x),color=grey,style=patchnogrid): quxian:=spacecurve([R*cos(t),R*sin(t),0],t=0..2*Pi,thickness=3,color=red): K:=8:for i from 0 to K do xi:=a+i*(b-a)/K: sanjiaoxing[i]:=spacecurve([[xi,g(xi),0],[xi,f(xi),0],[xi,(f(xi)+g(xi))/2,sqrt(3)/2*(f(xi)-g(xi))],[xi,g(xi),0]],thickness=3,color=blue): sanjiaoban[i]:=plot3d([xi,y,z],y=(f(xi)+g(xi))/2-(f(xi)-g(xi))/2+z/sqrt(3)..(f(xi)+g(xi))/2+(f(xi)-g(xi))/2-z/sqrt(3),z=0..sqrt(3)/2*(f(xi)-g(xi)),color=yellow,style=patchnogrid) od: sanjiaoxing:=display(seq(sanjiaoxing[i],i=0..K),insequence=false): sanjiaoban:=display(seq(sanjiaoban[i],i=0..K),insequence=false): qumian1:=plot3d([x,f(x)+(-f(x)+g(x))/2*t,(sqrt(3)/2)*(f(x)-g(x))*t],t=0..1,x=a..b,style=wireframe): qumian2:=plot3d([x,g(x)+(f(x)-g(x))/2*t,(sqrt(3)/2)*(f(x)-g(x))*t],t=0..1,x=a..b,style=wireframe): display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained,orientation=[-50,70]);null见同济《高等数学》6版，286页，18题现在来求这个 立体的体积nullnullwith(plots): f:=x->sin(x)+1: g:=x->sin(x-1)-1: a:=-Pi:b:=2*Pi: xzou:=spacecurve([x,0,0],x=a-1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=a-1..b+1,thickness=3,color=black): base:=plot3d([x,y,0],x=a..b,y=g(x)..f(x),color=grey,style=patchnogrid): quxianf:=spacecurve([x,f(x),0],x=a-1..b+1,thickness=3,color=red): quxiang:=spacecurve([x,g(x),0],x=a-1..b+1,thickness=3,color=red): K:=60:for i from 0 to K do xi:=a+i*(b-a)/K: zhengfangxing[i]:=spacecurve([[xi,g(xi),0],[xi,f(xi),0],[xi,f(xi),f(xi)-g(xi)],[xi,g(xi),f(xi)-g(xi)],[xi,g(xi),0]],thickness=3,color=blue): zhengfangban[i]:=plot3d([xi,y,z],y=g(xi)..f(xi),z=0..f(xi)-g(xi),color=yellow,style=patchnogrid): qumian1[i]:=plot3d([x,f(x),(f(x)-g(x))*t],t=0..1,x=a..xi,color=green): qumian2[i]:=plot3d([x,g(x),(f(x)-g(x))*t],t=0..1,x=a..xi,color=green): qumian3[i]:=plot3d([x,g(x)+(f(x)-g(x))*t,f(x)-g(x)],t=0..1,x=a..xi,color=green)od: zhengfangxing:=display(seq(zhengfangxing[i],i=0..K),insequence=true): zhengfangban:=display(seq(zhengfangban[i],i=0..K),insequence=true): qumian1:=display(seq(qumian1[i],i=0..K),insequence=true): qumian2:=display(seq(qumian2[i],i=0..K),insequence=true): qumian3:=display(seq(qumian3[i],i=0..K),insequence=true): display(xzou,yzou,base,quxianf,quxiang,zhengfangban,zhengfangxing,qumian1,qumian2,qumian3,scaling=constrained);动画的Maple程序nullnullnullnullwith(plots): R:=1.6: f:=x->sqrt(R^2-x^2): g:=x->-sqrt(R^2-x^2): a:=-R:b:=R:H:=2: xzou:=spacecurve([x,0,0],x=a-1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=a-1..b+1,thickness=3,color=black): base:=plot3d([x,y,0],x=a..b,y=g(x)..f(x),color=grey,style=patchnogrid): quxian:=spacecurve([R*cos(t),R*sin(t),0],t=0..2*Pi,thickness=3,color=red): K:=60:for i from 0 to K do xi:=a+i*(b-a)/K: zhengfangxing[i]:=spacecurve([[xi,g(xi),0],[xi,f(xi),0],[xi,f(xi),f(xi)-g(xi)],[xi,g(xi),f(xi)-g(xi)],[xi,g(xi),0]],thickness=3,color=blue): zhengfangban[i]:=plot3d([xi,y,z],y=g(xi)..f(xi),z=0..f(xi)-g(xi),color=yellow,style=patchnogrid): qumian1[i]:=plot3d([x,f(x),(f(x)-g(x))*t],t=0..1,x=a..xi,color=green): qumian2[i]:=plot3d([x,g(x),(f(x)-g(x))*t],t=0..1,x=a..xi,color=green): qumian3[i]:=plot3d([x,g(x)+(f(x)-g(x))*t,f(x)-g(x)],t=0..1,x=a..xi,color=grey)od: zhengfangxing:=display(seq(zhengfangxing[i],i=0..K),insequence=true): zhengfangban:=display(seq(zhengfangban[i],i=0..K),insequence=true): qumian1:=display(seq(qumian1[i],i=0..K),insequence=true): qumian2:=display(seq(qumian2[i],i=0..K),insequence=true): qumian3:=display(seq(qumian3[i],i=0..K),insequence=true): display(xzou,yzou,base,quxian,zhengfangban,zhengfangxing,qumian1,qumian2,qumian3,scaling=constrained,orientation=[-60,70]);动画的Maple程序null这个体积刚好等于牟合方盖的体积 见同济《高等数学》6版，下册143页，例4现在来求这个 立体的体积nullnullwith(plots): f:=x->sin(x)+2: g:=x->sin(x-1)-1: a:=-Pi:b:=2*Pi: xzou:=spacecurve([x,0,0],x=a-1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=-2..3,thickness=3,color=black): base:=plot3d([x,y,0],x=a..b,y=g(x)..f(x),color=grey,style=patchnogrid): quxianf:=spacecurve([x,f(x),0],x=a-1..b+1,thickness=3,color=red): quxiang:=spacecurve([x,g(x),0],x=a-1..b+1,thickness=3,color=red): K:=60:for i from 0 to K do xi:=a+i*(b-a)/K: banyuan[i]:=spacecurve([xi,(f(xi)+g(xi))/2+(f(xi)-g(xi))/2*cos(t),(f(xi)-g(xi))/2*sin(t)],t=0..Pi,thickness=3,color=blue): dixian[i]:=spacecurve([xi,y,0],y=g(xi)..f(xi),thickness=3,color=blue): banyuanban[i]:=plot3d([xi,(f(xi)+g(xi))/2+r*cos(t),r*sin(t)],r=0..(f(xi)-g(xi))/2,t=0..Pi,color=yellow,style=patchnogrid): qumian[i]:=plot3d([x,(f(x)+g(x))/2+(f(x)-g(x))/2*cos(t),(f(x)-g(x))/2*sin(t)],t=0..Pi,x=a..xi,color=green)od: banyuan:=display(seq(banyuan[i],i=0..K),insequence=true): dixian:=display(seq(dixian[i],i=0..K),insequence=true): banyuanban:=display(seq(banyuanban[i],i=0..K),insequence=true): qumian:=display(seq(qumian[i],i=0..K),insequence=true): display(xzou,yzou,quxianf,quxiang,banyuanban,base,banyuan,qumian,dixian,scaling=constrained);动画的Maple程序nullnullwith(plots): f:=x->sin(x)+2: g:=x->sin(x-1)-1: a:=-Pi:b:=2*Pi: xzou:=spacecurve([x,0,0],x=a-1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=-2..3,thickness=3,color=black): quxianf:=spacecurve([x,f(x),0],x=a-1..b+1,thickness=3,color=red): quxiang:=spacecurve([x,g(x),0],x=a-1..b+1,thickness=3,color=red): K:=60:for i from 0 to K do xi:=a+i*(b-a)/K: banyuan[i]:=spacecurve([xi,(f(xi)+g(xi))/2+(f(xi)-g(xi))/2*cos(t),(f(xi)-g(xi))/2*sin(t)],t=0..Pi,thickness=3,color=blue): dixian[i]:=spacecurve([xi,y,0],y=g(xi)..f(xi),thickness=3,color=blue): banyuanban[i]:=plot3d([xi,(f(xi)+g(xi))/2+r*cos(t),r*sin(t)],r=0..(f(xi)-g(xi))/2,t=0..Pi,color=yellow,style=patchnogrid): base[i]:=plot3d([x,y,0],x=a..xi,y=f(x)..g(x),color=gray,style=patchnogrid): qumian[i]:=plot3d([x,(f(x)+g(x))/2+(f(x)-g(x))/2*cos(t),(f(x)-g(x))/2*sin(t)],t=0..Pi,x=a..xi,color=green)od: banyuan:=display(seq(banyuan[i],i=0..K),insequence=true): dixian:=display(seq(dixian[i],i=0..K),insequence=true): base:=display(seq(base[i],i=0..K),insequence=true): banyuanban:=display(seq(banyuanban[i],i=0..K),insequence=true): qumian:=display(seq(qumian[i],i=0..K),insequence=true): display(xzou,yzou,quxianf,quxiang,banyuanban,base,banyuan,qumian,dixian,scaling=constrained);动画的Maple程序nullnullwith(plots): A:=2:B:=1: a:=-A:b:=A: f:=x->(B/A)*sqrt(A^2-x^2): g:=x->-(B/A)*sqrt(A^2-x^2): xzou:=spacecurve([x,0,0],x=-A-.5..A+.5,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=-B-.5..B+.5,thickness=3,color=black): base:=plot3d([x,y,0],x=a..b,y=g(x)..f(x),color=grey,style=patchnogrid): quxian:=spacecurve([A*cos(t),B*sin(t),0],t=0..2*Pi,thickness=3,color=red): K:=60:for i from 0 to K do xi:=a+i*(b-a)/K: banyuan[i]:=spacecurve([xi,(f(xi)+g(xi))/2+(f(xi)-g(xi))/2*cos(t),(f(xi)-g(xi))/2*sin(t)],t=0..Pi,thickness=3,color=blue): dixian[i]:=spacecurve([xi,y,0],y=g(xi)..f(xi),thickness=3,color=blue): banyuanban[i]:=plot3d([xi,(f(xi)+g(xi))/2+r*cos(t),r*sin(t)],r=0..(f(xi)-g(xi))/2,t=0..Pi,color=yellow,style=patchnogrid): qumian[i]:=plot3d([x,(f(x)+g(x))/2+(f(x)-g(x))/2*cos(t),(f(x)-g(x))/2*sin(t)],t=0..Pi,x=a..xi,color=green)od: banyuan:=display(seq(banyuan[i],i=0..K),insequence=true): dixian:=display(seq(dixian[i],i=0..K),insequence=true): banyuanban:=display(seq(banyuanban[i],i=0..K),insequence=true): qumian:=display(seq(qumian[i],i=0..K),insequence=true): display(xzou,yzou,quxian,banyuanban,base,banyuan,qumian,dixian,scaling=constrained,orientation=[-50,70]);动画的Maple程序