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Re: Help for solving this Integrate[Sqrt[t*(1-t)*

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112821] Re: Help for solving this Integrate[Sqrt[t*(1-t)*
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sat, 2 Oct 2010 05:43:44 -0400 (EDT)

Assuming that you intend for the Sqrt to encompass the entire argument,

$Version

"7.0 for Mac OS X x86 (64-bit) (February 19, 2009)"

Plot3D[Sqrt[t*(1 - z)*(t - z)],
 {z, 0, 2}, {t, 0, 2}]

Assuming[#, Integrate[Sqrt[t*(1 - z)*(t - z)],
    {t, 0, z}]] & /@
 {{0 < z}, {0 < z < 1}, {1 < z}}

{-((z^2*(2*I*Sqrt[1/(1 - z)]*
         Sqrt[-1 + z]*
                Log[2*I*Sqrt[z]] + 
        Log[4*z]))/
        (8*Sqrt[1/(1 - z)])), 
 (1/8)*I*Pi* Sqrt[1 - z]*z^2, 
 (1/8)*Pi*Sqrt[-1 + z]*z^2}


Bob Hanlon

---- Hugo <hpe650820 at gmail.com> wrote: 

=============
Could any body help me to solve the following integral in
mathematica?

Integrate[sqrt[t * (1-z)*(t-z),{t,0,z}];  t and z are reals; z>0

I did make a mistake posting the wrong equation yesterday, I apologize
for that.

Any help would be appreciate,

Hugo




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