曲线围成的区域分析和讲解

1、曲线围成的区域分析和讲解X型区域用 Filling曲线下方的区域Plotfx,x,a,b,Filling-Bottom,FillingStyle-Yellowfx_:=x2;Quxian=Plotfx,x,-0.1,1.1,PlotStyle-AbsoluteThickness2,Red;Quyu=Plotfx,x,0,1,Filling-Bottom,AspectRatio-1,PlotRange-All,Ticks-1,0,1,-1,0,1,FillingStyle-Green;ShowQuyu,Quxian30 JUN 2010曲线与x轴围成的区域Plotfx,x,a,b,Filling

2、-Axis,FillingStyle-Yellow fx_:=Sinx;Quxian=Plotfx,x,-1.1,1.1,PlotStyle-AbsoluteThickness3,Red;Quyu=Plotfx,x,-1,1,Filling-Axis,AspectRatio-1,PlotRange-All,Ticks-1,0,1,-1,0,1,FillingStyle-Green;ShowQuyu,Quxian30 JUN 2010两曲线围成的区域Quyu=Plotfx,gx,x,a,b,Filling-1 fx_:=x;gx_:=x2;Quxian1=Plotfx,x,-1.3,1.3,Pl

3、otStyle-AbsoluteThickness2,Red;Quxian2=Plotgx,x,-1.3,1.3,PlotStyle-AbsoluteThickness2,Blue;Quyu=Plotfx,gx,x,0,1,Filling-1-2,AspectRatio-1,PlotRange-All,Ticks-1,0,1,-1,0,1,FillingStyle-Green;ShowQuyu,Quxian1,Quxian230 JUN 2010 fx_:=Sinx;gx_:=Cosx;Quxian1=Plotfx,x,0,2 Pi,PlotStyle-AbsoluteThickness2,R

4、ed;Quxian2=Plotgx,x,0,2Pi,PlotStyle-AbsoluteThickness2,Blue;Quyu=Plotfx,gx,x,0,2Pi,Filling-1-2,AspectRatio-.8,PlotRange-All,Ticks-0,Pi/2,Pi,3Pi/2,2 Pi,-1,0,1,FillingStyle-Yellow;ShowQuyu,Quxian1,Quxian230 JUN 2010 fx_:=SinPi x Exp-(x-1)2;gx_:=4Cosx-2;Quxian1=Plotfx,x,0,4,PlotStyle-AbsoluteThickness2

5、,Red;Quxian2=Plotgx,x,0,4,PlotStyle-AbsoluteThickness2,Blue;Quyu=Plotfx,gx,x,0.6,3.6,Filling-1-2,AspectRatio-1,PlotRange-All,Ticks-0,1,2,3,4,-1,0,1,2,3,4,FillingStyle-LightRed,AxesOrigin-0,0;ShowQuyu,Quxian1,Quxian230 JUN 2010 fx_:=x;gx_:=x3;Quxian1=Plotfx,x,-1.3,1.3,PlotStyle-AbsoluteThickness2,Red

6、;Quxian2=Plotgx,x,-1.3,1.3,PlotStyle-AbsoluteThickness2,Red;Quyu=Plotfx,gx,x,-1,1,Filling-1-2,AspectRatio-1.4,PlotRange-All,Ticks-1,0,1,-1,0,1,FillingStyle-Green;ShowQuyu,Quxian1,Quxian230 JUN 2010X型区域用 RegionPlot曲线下方的区域 fx_:=x2;Quxian=Plotfx,x,-1,1.1,PlotStyle-AbsoluteThickness4,Red;Quyu=RegionPlot

7、0yGreen;ShowQuyu,Quxian,PlotRange-All,Axes-Automatic,AspectRatio-0.7,Frame-False,Ticks-1,0,1,0,1,230 JUN 2010曲线与x轴围成的区域 fx_:=Sinx;Quxian=Plotfx,x,-4,4,PlotStyle-AbsoluteThickness3,Red;Quyu=RegionPlotfxy0 ,x,-Pi,Pi ,y,-1,1,PlotStyle-Cyan;Quyu2=RegionPlotfxyGreen;ShowQuyu,Quyu2,Quxian,PlotRange-All,Ax

8、es-Automatic,AspectRatio-1,Frame-False,Ticks-Pi,-Pi/2,0,Pi/2,Pi,-1,0,130 JUN 2010两曲线围成的区域 fx_:=x;gx_:=x2;Quxian=Plotfx,x,-0.1,1.1,PlotStyle-AbsoluteThickness3,Red;Quxian2=Plotgx,x,-0.1,1.1,PlotStyle-AbsoluteThickness3,Blue;Quyu=RegionPlotgxyGreen;ShowQuyu,Quxian,Quxian2,PlotRange-All,Axes-Automatic,

9、AspectRatio-1,Frame-False,Ticks-1,0,1,0,1,230 JUN 2010 fx_:=x+1/2;gx_:=x2+1/5;Quxian=Plotfx,x,0.1,1,PlotStyle-AbsoluteThickness3,Red;Quxian2=Plotgx,x,0.1,1,PlotStyle-AbsoluteThickness3,Blue;Quyu=RegionPlotgxyGreen;ShowQuyu,Quxian,Quxian2,PlotRange-All,Axes-True,AxesOrigin-0,0,AspectRatio-1,Frame-Fal

10、se,Ticks-1/2,0,1/2,1,0,1/1,1,3/230 JUN 201030 JUN 2010 fx_:=Sinx;gx_:=Cosx;Quxian=Plotfx,x,0,2Pi,PlotStyle-AbsoluteThickness3,Red;Quxian2=Plotgx,x,0,2Pi,PlotStyle-AbsoluteThickness3,Blue;Quyu=RegionPlotfxygx ,x,0,2Pi ,y,-1,1,PlotStyle-Pink;Quyu2=RegionPlotfxyGreen;ShowQuyu,Quyu2,Quxian,Quxian2,PlotR

11、ange-All,Axes-Automatic,AspectRatio-1,Frame-False,Ticks-0,Pi/2,Pi,3Pi/2,2Pi,-1,0,1 fx_:=SinPi x Exp-(x-1)2;gx_:=4Cosx-2;Quxian=Plotfx,x,0,4,PlotStyle-AbsoluteThickness3,Red;Quxian2=Plotgx,x,0,4,PlotStyle-AbsoluteThickness3,Blue;Quyu=RegionPlotfxyGreen;ShowQuyu,Quxian,Quxian2,PlotRange-All,Axes-Autom

12、atic,AspectRatio-1,Frame-False,Ticks-1,0,1,2,3,4,-3,-2,-1,0,1,2,3,430 JUN 201030 JUN 2010 fx_:=x;gx_:=x3;Quxian=Plotfx,x,-1.2,1.2,PlotStyle-AbsoluteThickness3,Red;Quxian2=Plotgx,x,-1.2,1.2,PlotStyle-AbsoluteThickness3,Blue;Quyu=RegionPlotfxygx,x,-1.2,1.2,y,-1,1,PlotStyle-Pink;Quyu2=RegionPlotfxyGree

13、n;ShowQuyu,Quyu2,Quxian,Quxian2,PlotRange-All,Axes-Automatic,AspectRatio-1.2,Frame-False,Ticks-1,-1/2,0,1/2,1,-1,-1/2,0,1/2,1Y型区域 fy_:=Siny;Quxian=ParametricPlotfy,y,y,0,Pi,PlotStyle-AbsoluteThickness3,Red;Quyu=RegionPlotfyx0,x,0,1,y,0,Pi,PlotStyle-Green;ShowQuyu,Quxian,PlotRange-All,Axes-Automatic,

14、AspectRatio-1.7,Frame-False,Ticks-0,1/2,1,0,Pi/2,Pi30 JUN 2010 fy_:=12 (y2-y3);Quxian=ParametricPlotfy,y,y,0,1,PlotStyle-AbsoluteThickness3,Red;Quyu=RegionPlotfyx0,x,0,5,y,0,1,PlotStyle-Green;ShowQuyu,Quxian,PlotRange-All,Axes-Automatic,AspectRatio-0.7,Frame-False,Ticks-0,1,2,0,1/2,130 JUN 2010 fy_:

15、=y2/2;gy_:=y4/4-y2/2;Quxian=ParametricPlotfy,y,y,0,2.3,PlotStyle-AbsoluteThickness3,Red;Quxian2=ParametricPlotgy,y,y,0,2.1,PlotStyle-AbsoluteThickness3,Blue;Quyu=RegionPlotfyxgy,x,-1/2,2,y,0,2.3,PlotStyle-Green;ShowQuyu,Quxian,Quxian2,PlotRange-All,Axes-Automatic,AspectRatio-0.7,Frame-False,Ticks-0,

16、1,2,0,1,230 JUN 2010 fy_:=y2+1;gy_:=y4+1/2;Quxian=ParametricPlotfy,y,y,0,1,PlotStyle-AbsoluteThickness3,Red;Quxian2=ParametricPlotgy,y,y,0,1,PlotStyle-AbsoluteThickness3,Blue;Quyu=RegionPlotfyxgy,x,-1/2,2,y,0.4,0.8,PlotStyle-Green;ShowQuyu,Quxian,Quxian2,PlotRange-All,Axes-True,AxesOrigin-0,0,Aspect

17、Ratio-1,Ticks-0,1,2,0,1/2,1,Frame-False30 JUN 2010 fy_:=Siny;gy_:=(1-y) y+1;Quxian=ParametricPlotfy,y,y,0,2.1,PlotStyle-AbsoluteThickness3,Red;Quxian2=ParametricPlotgy,y,y,0,2.1,PlotStyle-AbsoluteThickness3,Blue;Quyu=RegionPlotfyxgy,x,-1,2,y,0,2,PlotStyle-Green;Quyu2=RegionPlotfyxPink;ShowQuyu,Quyu2

18、,Quxian,Quxian2,PlotRange-All,Axes-Automatic,AspectRatio-0.7,Frame-False,30 JUN 2010 fy_:=y2;gy_:=1;Quxian=ParametricPlotfy,y,y,-1.2,1.2,PlotStyle-AbsoluteThickness3,Red;Quxian2=ParametricPlotgy,y,y,-1.2,1.2,PlotStyle-AbsoluteThickness3,Blue;Quyu=RegionPlotfyxCyan;ShowQuyu,Quxian,Quxian2,PlotRange-A

19、ll,Axes-Automatic,AspectRatio-1.5,Frame-False,Ticks-0,1/2,1,-1,0,130 JUN 2010多边形区域 fx_,y_:=x+y;gx_,y_:=x-2y;Quyu=RegionPlot-2fx,y2 & 1gx,yGreen,PlotPoints-100;ShowQuyu,PlotRange-2,3,-2,1,AxesOrigin-0,0,Axes-True,AspectRatio-0.7,Frame-False,Ticks-1,0,1,2,3,-2,-1,0,1,22 JULY 2010fx_,y_:=y/x2;gx_,y_:=x

20、2+y2 ;Quyu=RegionPlot1fx,y4 & 1gx,yGreen,PlotPoints-100;ShowQuyu,PlotRange-0,2,0,2,AxesOrigin-0,0,Axes-True,AspectRatio-1,Frame-False,Ticks-1,2,3,0,1,22 JULY 2010 fx_,y_:=y/x2;gx_,y_:=x2+y2 ;Quxian1=Plot1 x2,x,0,2,PlotStyle-Red,AbsoluteThickness2;Quxian2=Plot4 x2,x,0,2,PlotStyle-Red,AbsoluteThicknes

21、s2;Quxian3=ParametricPlotCost,Sint,t,0,Pi/2,PlotStyle-Blue,AbsoluteThickness2;Quxian4=ParametricPlot2 Cost,2 Sint,t,0,Pi/2,PlotStyle-Blue,AbsoluteThickness2;Quyu=RegionPlot1fx,y4 & 1gx,yGreen;ShowQuyu,Quxian1,Quxian2,Quxian3,Quxian4,PlotRange-0,2,0,2,AxesOrigin-0,0,Axes-True,AspectRatio-1,Frame-Fals

22、e,Ticks-1,2,3,0,1,22 JULY 2010 fx_,y_:=y/x2;gx_,y_:=x/y2 ;Quxian1=Plot1 x2,x,0,2,PlotStyle-Red,AbsoluteThickness2;Quxian2=Plot4 x2,x,0,2,PlotStyle-Red,AbsoluteThickness2;Quxian3=ParametricPlot y2,y,y,0,2,PlotStyle-Blue,AbsoluteThickness2;Quxian4=ParametricPlot 4y2,y,y,0,2,PlotStyle-Blue,AbsoluteThic

23、kness2;Quyu=RegionPlot1fx,y4 & 1gx,yGreen;ShowQuyu,Quxian1,Quxian2,Quxian3,Quxian4,PlotRange-0,2,0,2,AxesOrigin-0,0,Axes-True,AspectRatio-1,Frame-False,Ticks-1,2,3,0,1,22 JULY 2010曲边扇形区域 Quyu=RegionPlotx2+y20,x,-4,4,y,-4,4,PlotStyle-Cyan;ShowQuyu,PlotRange-3,3,-0,3,Axes-Automatic,AspectRatio-0.7,Fra

24、me-False,Ticks-2,-1,0,1,2,-2,-1,0,1,22 July 2010 Quyu=RegionPlot1x2+y2Cyan;ShowQuyu,PlotRange-3,3,-3,3,Axes-Automatic,AspectRatio-1,Frame-False,Ticks-2,-1,0,1,2,-2,-1,0,1,22 July 2010 Quyu=RegionPlotx2+y25 & yx/2 & x0,x,-4,4,y,-4,4,PlotStyle-Cyan;ShowQuyu,PlotRange-0,3,-0,3,Axes-Automatic,AspectRati

25、o-1,Frame-False,Ticks-2,-1,0,1,2,-2,-1,0,1,22 July 2010 Quxian1=PolarPlot4 Sint,t,0,2Pi,PlotStyle-Red,AbsoluteThickness3;Quxian2=PolarPlot2 ,t,0,2Pi,PlotStyle-Red,AbsoluteThickness3;Quyu=RegionPlotx2+(y-2)24 & x2+y2Gray;Quyu2=RegionPlotx2+(y-2)2Yellow;Quyu3=RegionPlot x2+y2Pink;ShowQuyu3,Quyu2,Quyu,

26、Quxian1,Quxian2,PlotRange-2,2,-2,4,Axes-Automatic,AspectRatio-1.4,Frame-False,Ticks-2,-1,0,1,2,-2,-1,0,1,2,3,42 July 20102 July 2010利用参数方程绘制平面区域(1) 利用平面参数方程绘制平面区域 Quyu=ParametricPlotx,y,x,1,2,y,x,x2,PlotStyle-Blue;ShowQuyu,PlotRange-0,3,0,5,Axes-Automatic,AspectRatio-1.5,Frame-False,Ticks-0,1,2,3,0,

27、1,2,3,4,52 July 2010利用平面参数方程绘制平面区域 Quyu=ParametricPlotr Cost,r Sint,t,0.05Pi,0.35Pi,r,1,Sint,PlotStyle-Black;ShowQuyu,PlotRange-0,1,0,1,Axes-Automatic,AspectRatio-1,Frame-False,Ticks-0,1,0,12 July 2010利用参数方程绘制平面区域 Quyu=ParametricPlotr Cost,r Sint,t,-Pi/6,Pi/3,r,Cost,2Cost,PlotStyle-Black;ShowQuyu,Pl

28、otRange-1,2,-1,2,Axes-Automatic,AspectRatio-1,Frame-False,Ticks-1,0,1,2,-1,0,1,2两圆和两直线所围的区域2 July 2010 Quyu=ParametricPlotr Cost,r Sint,t,Pi/6,Pi/2,r,1+Sint,3Cost,PlotStyle-Black,PlotPoints-30;ShowQuyu,PlotRange-1,3,-1,3,Axes-Automatic,AspectRatio-1,Frame-False,Ticks-1,0,1,2,-1,0,1,2两圆和两直线所围的区域 2 Ju

29、ly 2010 Quyu=ParametricPlotr Cost,r Sint,t,Pi/6,5Pi/6,r,1+Sint,3Sint;ShowQuyu,PlotRange-2,2,-1,3,Axes-Automatic,AspectRatio-1,Frame-False,Ticks-2,-1,0,1,2,-1,0,1,2,3,4心形线和圆所围的区域2 July 2010(2) 利用3D参数方程绘制平面区域Quyu=ParametricPlot3Dx,y,0,x,1,2,y,x,x2,PlotStyle-Red,Mesh-False;ShowQuyu,PlotRange-0,3,0,5,0,

30、0.01,Axes-Automatic,AspectRatio-1.4,Ticks-0,1,2,3,0,1,2,3,4,5,ViewPoint-0,0,1,Boxed-False2 July 2010 fx_:=x+1/2;gx_:=x2+1/5;Quxian1=ParametricPlot3Dx,fx,0,x,0,1.2,PlotStyle-AbsoluteThickness3,Red;Quxian2=ParametricPlot3Dx,gx,0,x,0,1.2,PlotStyle-AbsoluteThickness3,Blue;Quyu=ParametricPlot3Dx,y,0,x,0.

31、3,1,y,fx,gx,PlotStyle-LightGray,Mesh-False;ShowQuyu,Quxian1,Quxian2,PlotRange-0,1.2,0,1.6,0,0.01,Axes-Automatic,AspectRatio-1.3,Ticks-0.5,1,0,0.5,1,1.5,2,ViewPoint-0,0,1,Boxed-False,AxesOrigin-0,0,02 July 2010 fx_:=Sinx;gx_:=Cosx;Quxian1=ParametricPlot3Dx,fx,0,x,0,2Pi,PlotStyle-AbsoluteThickness3,Re

32、d;Quxian2=ParametricPlot3Dx,gx,0,x,0,2Pi,PlotStyle-AbsoluteThickness3,Blue;Quyu=ParametricPlot3Dx,y,0,x,0.2,1.8Pi,y,fx,gx,PlotStyle-LightYellow,Mesh-False,PlotPoints-50;ShowQuyu,Quxian1,Quxian2,PlotRange-0,2Pi,-1.2,1.2,0,0.01,Axes-Automatic,AspectRatio-0.4,Ticks-Pi/2,Pi,3Pi/2,2Pi,0,1,ViewPoint-0,0,1

33、,Boxed-False,AxesOrigin-0,0,02 July 2010 fy_:=y2+1;gy_:=y4+1/2;Quxian=ParametricPlot3Dfy,y,0,y,0,1,PlotStyle-AbsoluteThickness3,Red;Quxian2=ParametricPlot3Dgy,y,0,y,0,1,PlotStyle-AbsoluteThickness3,Blue;Quyu=ParametricPlot3Dx,y,0,y,0.2,0.8,x,gy,fy,PlotStyle-Yellow,Mesh-False;ShowQuyu,Quxian,Quxian2,

34、PlotRange-0,2,0,1.2,0,0.01,Axes-Automatic,AspectRatio-.6,Ticks-0.5,1,1.5,2,0,0.5,1,ViewPoint-0,0,1,Boxed-False,AxesOrigin-0,0,02 July 2010 fy_:=Siny;gy_:=(1-y) y+1;Quxian=ParametricPlot3Dfy,y,0,y,0,2.1,PlotStyle-AbsoluteThickness3,Red;Quxian2=ParametricPlot3Dgy,y,0,y,0,2.1,PlotStyle-AbsoluteThickness3,Blue;Quyu=ParametricPlot3Dx,y,0,y,0.2,2,x,gy,fy,PlotStyle-LightBlue,Mesh-False;ShowQuyu,Quxian,Quxian2,PlotRange-1.5,1.5,0,2.4,0,0.01,Axes-Automatic,AspectRatio-0.8,Ticks-1.5,-1,-0.5,0,0.5,1,1.5,2,0.5,1,1.5,2,2.5,ViewPoint-0,0,1,Boxed-False,AxesOrigin-0,0,02 JULY 2010 r1t_:=1+Sint;r2t_:=3*S