Definite integrals in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg72145] Definite integrals in Mathematica*From*: some guy named Dave <nuclearwhippingboy at hotmail.com>*Date*: Wed, 13 Dec 2006 06:40:29 -0500 (EST)

Hey all, Hmm, I tried posting this yesterday, but it hasn't shown up yet. So, appologies if this gets double-posted. I'm a newbie to Mathematica, and I have a function that I want to integrate. It's basically a smoothing function over a vector space, and I want to normalize it. The function itself looks like this: f(r) = (h^2 - r^2)^3 where r is the scalar length ||x|| of some displacement vector x, and h is a constant. We are really only interested in values of r in [0,h], and for 2D vectors. However, I have some research literature involving 3D vectors that I want to compare against, just for sanity. So, if x is a 3D vector, then the surface of the sphere at radius r should be (4/3)(f(r))^3. We should then be able to get the definite integral from Mathematica by doing something like: Integrate[ 4/3 * Pi( (h^2 - r^2)^3 )^3, {r, 0, h}] When I do so, I get back 262144 pi h^19 / 692835 However, the literature I have says that the integral should yield 64 pi h^9 / 315 So, have I screwed something up? Is the literature wrong, perhaps? Thanks. Dave

**Follow-Ups**:**Re: Definite integrals in Mathematica***From:*Darren Glosemeyer <darreng@wolfram.com>