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已知平行截面的面积求体积

2012-07-02 21:12:38| 分类：数学专题讲解 | 标签： |举报 |字号大中小订阅

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with(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);

with(plots):

R:=1:

f:=x->sqrt(R^2-x^2):

g:=x->-sqrt(R^2-x^2):

a:=-R:b:=R:

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]);

with(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);

R:=1.6:

f:=x->sqrt(R^2-x^2):

g:=x->-sqrt(R^2-x^2):

a:=-R:b:=R:

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]);

with(plots):

R:=1.6:

f:=x->sqrt(R^2-x^2):

g:=x->-sqrt(R^2-x^2):

a:=-R:b:=R:

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]);

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