[mg84549] Re: Integrating "If"

[Scott Hemphill <hemphill at hemphills.net>]

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