已知平行截面面積求立體的體積圖形、動(dòng)畫、計(jì)算-預(yù)覽頁(yè)
【正文】 ,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:=*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*(1z/H)..(f(xi)+g(xi))/2+(f(xi)g(xi))/2*(1z/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])。 動(dòng)畫的 Maple程序 July 1, 2022 四川大學(xué)數(shù)學(xué)學(xué)院 徐小湛 切片法 13 2213( ) ( ( ) ( ) )223( sin c os 4)4 2 3A x f x g xxx? ? ?? ? ?截 面 面 積1 7 3 2 7 9( ) 2 8 . 8 12 1 6V A x d x????? ? ? ??立 體 體 積?? ?d???????? ??14 3???? ?????? ? ?? ????? ????si n x2???? ????c o s x3 42x ? ?? ?27916 17 3 ?2???2 8 .8 1 4 3 8 3 7 9 2 8 .8 1 4 3 8 3 8 1f:=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)。 動(dòng)畫的 Maple程序 July 1, 2022 四川大學(xué)數(shù)學(xué)學(xué)院 徐小湛 切片法 16 R:=: f:=xsqrt(R^2x^2): g:=xsqrt(R^2x^2): a:=R:b:=R:H:=2: xzou:=spacecurve([x,0,0],x=a1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=a1..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:=*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))/2z/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])。 動(dòng)畫的 Maple程序 July 1, 2022 四川大學(xué)數(shù)學(xué)學(xué)院 徐小湛 切片法 21 xy( ) sin 1f x x??( ) s in ( 1) 1g x x? ? ? July 1, 2022 四川大學(xué)數(shù)學(xué)學(xué)院 徐小湛 切片法 22 ( ) sin 1f x x??x( ) s in ( 1) 1g x x? ? ?y July 1, 2022 四川大學(xué)數(shù)學(xué)學(xué)院 徐小湛 切片法 23 xy2 2 26 x y R xx??例 立 體 以 圓 為 底 ， 在 處 的垂 直 于 軸 的 截 面 是 一 個(gè) 正 方 形 。 動(dòng)畫的 Maple程序 July 1, 2022 四川大學(xué)數(shù)學(xué)學(xué)院 徐小湛 切片法 28 ( ) sin + 2f x x?x( ) s in ( 1) 1g x x? ? ?y July 1, 2022 四川大學(xué)數(shù)學(xué)學(xué)院 徐小湛 切片法 29 with(plots): f:=xsin(x)+2: g:=xsin(x1)1: a:=Pi:b:=2*Pi: xzou:=spacecurve([x,0,0],x=a1..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=a1..b+1,thickness=3,color=red): quxiang:=spacecurve([x,g(x),0],x=a1..b+1,thickness=3,color=red): K:=60:for i from 0 to K do xi:=a+i*(ba)/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=constrai
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