Mathematica 9 is now available
Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2010

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Help for solving this Integrate[Sqrt[t*(1-t)* (t-z),{t,0,z} ] NEW!!!!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112837] Re: Help for solving this Integrate[Sqrt[t*(1-t)* (t-z),{t,0,z} ] NEW!!!!
  • From: Curtis Osterhoudt <cfo at lanl.gov>
  • Date: Sat, 2 Oct 2010 05:46:44 -0400 (EDT)

In[13]:= Integrate[Sqrt[t*(1 - z)*(t - z)], {t, 0, z}, 
 Assumptions -> z > 0]

Out[13]= 1/8 \[Pi] Sqrt[-1 + z] z^2


It helped me a great deal to plot both the integral and the answers (especially the integral) vs. t, with various values of z. Then I recognized the integrand can be cast into a slightly different form:

Integrate[Sqrt[-1*((t - z/2)^2 - z^2/4)], {t, 0, z}, 
 Assumptions -> z > 0 && 0 <= t <= z]

The integral gives 
(\[Pi] z^2)/8

which is simply the area of half a circle with radius z/2; the circles are obvious if you plot the integrand. They're later scaled by the Sqrt[z-1] factor. 

On Friday, October 01, 2010 03:41:39 Hugo 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
> 
> 


-- 
==================================
Curtis Osterhoudt
cfo at remove_this.lanl.and_this.gov
==================================


  • Prev by Date: Re: BSpline function
  • Next by Date: Re: Plotting feasible region of a linear programme
  • Previous by thread: Re: Help for solving this Integrate[Sqrt[t*(1-t)* (t-z),{t,0,z} ] NEW!!!!
  • Next by thread: Re: Help for solving this Integrate[Sqrt[t*(1-t)* (t-z),{t,0,z} ] NEW!!!!