Volume integration pb

*To*: mathgroup at smc.vnet.net*Subject*: [mg104083] Volume integration pb*From*: Fred Bartoli <""@news.free.fr>*Date*: Sun, 18 Oct 2009 05:28:46 -0400 (EDT)*Reply-to*: myname_with_a_dot_inbetween at free.fr

Integrating (r^2 - 2 z^2)/(3 (r^2 + z^2)^(5/2)) over a cylinder of R radius and -h/2 to +h/2 height. (* Integrating first over radius then over height : *) Integrate[2\[Pi] r (r^2-2 z^2)/(3 (r^2+z^2)^(5/2)),{r,0,R},Assumptions->R>0&&z>0]; int1=Integrate[%,{z,-h/2,h/2},Assumptions->R>0&&h>0] (* Then integrating first over height then over radius : *) Integrate[(r^2 - 2 z^2)/(3 (r^2 + z^2)^(5/2)), {z, -h/2, h/2}, Assumptions -> h > 0 && r > 0] int2 = Integrate[2 \[Pi] r %, {r, 0, R}, Assumptions -> h > 0 && R > 0] int2-int1//Simplify -> 4 Pi/3 Am I missing something? -- Thanks, Fred.