Re: Integrating "If"
- To: mathgroup at smc.vnet.net
- Subject: [mg84549] Re: Integrating "If"
- From: Scott Hemphill <hemphill at hemphills.net>
- Date: Thu, 3 Jan 2008 20:26:10 -0500 (EST)
- References: <flc7vh$809$1@smc.vnet.net> <flfubb$jrm$1@smc.vnet.net> <flie4b$fit$1@smc.vnet.net>
- Reply-to: hemphill at alumni.caltech.edu
Scott Hemphill <hemphill at hemphills.net> writes: > "David W.Cantrell" <DWCantrell at sigmaxi.net> writes: >> BTW, what did you get by hand eventually? > > If 0 <= d <= 1, then > > (-8*d^3)/3 + d^4/2 + d^2*Pi > > If 1 <= d <= Sqrt[2], then > > 1/3 - 2*d^2 - d^4/2 + (4*Sqrt[-1 + d^2]*(1 + 2*d^2))/3 + Pi + > 2*(-1 + d^2)*ArcCot[Sqrt[-1 + d^2]] - 2*(1 + d^2)*ArcTan[Sqrt[-1 + d^2]] This last formula can be simplified a bit more: 1/3 - 2*d^2 - d^4/2 + (4*Sqrt[-1 + d^2]*(1 + 2*d^2))/3 + d^2*Pi - 4*d^2*ArcSec[d] Scott -- Scott Hemphill hemphill at alumni.caltech.edu "This isn't flying. This is falling, with style." -- Buzz Lightyear