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