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Re: Help for solving this Integrate[Sqrt[t*(1t)* (tz),{t,0,z} ] NEW!!!!
Posted:
Oct 2, 2010 5:46 AM


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[z1] 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 * (1z)*(tz),{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@remove_this.lanl.and_this.gov ==================================



