Wolfram Cloud Document

In[]:=

UFO::usage="To get the volume use the disk method:

V

i

=π[f(x)

2

]

dx o

V

i

=π[f(y)

2

]

dy";ContourPloty==

-

1

4

x^2



+1,y==1-1

1-

2

x

25

,y==1,{x,0,5},{y,0,2},AspectRatio->Automatic

Out[]=

In[]:=

F[t_]:=

-

1

4

t^2



+1;G[t_]:=1-1

1-

2

t

25

;H[t_]:=1;gr=Show[surf1=RevolutionPlot3D[F[t],{t,0,5},MeshNone,AxesFalse,PlotRangeAll,ColorFunction"LightTemperatureMap",BoxedFalse],surf2=RevolutionPlot3D[G[t],{t,0,5},MeshNone,AxesFalse,PlotRangeAll,ColorFunction"LightTemperatureMap",BoxedFalse],surf3=RevolutionPlot3D[H[t],{t,0,5},PlotRangeAll,MeshNone,AxesFalse,ColorFunction"LightTemperatureMap",BoxedFalse]]

Out[]=

In[]:=

V=N

1

∫

0

π

2

5

1-(y-1)^2



y+

2

∫

1

π

2



-4Log[y-1]



y

Out[]=

64.9262

In[]:=

ResourceFunction["SpinShow"][gr,30]

Out[]=