A negative volume!
- To: mathgroup at yoda.physics.unc.edu
- Subject: A negative volume!
- From: "Roger B. Kirchner" <kirchner at cs.umn.edu>
- Date: Tue, 10 Mar 92 10:55:22 -0600
Let V be the volume of the solid inside the first octant of the unit
sphere and outside the cylinder with cylindrical equation r = Sin[t].
Computing in cylindrical coordinates,
In[1]:= Integrate[r, {z, 0, (1 - r^2)^(1/2)}]
2
Out[1]= r Sqrt[1 - r ]
In[2]:= Integrate[%, {r, Sin[t], 1}]
2 2
Cos[t] Sqrt[Cos[t] ]
Out[2]= ---------------------
3
In[3]:= Integrate[%, {t, 0, Pi/2}]
2
Out[3]= -(-)
9
Thus V = -2/9!
Anybody have any suggestions on how to avoid this kind of problem?
Roger Kirchner