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Re: Different results for same integration
*To*: mathgroup at smc.vnet.net
*Subject*: [mg73003] Re: Different results for same integration
*From*: "ashesh" <ashesh.cb at gmail.com>
*Date*: Sun, 28 Jan 2007 01:19:56 -0500 (EST)
*References*: <epcoj2$8gh$1@smc.vnet.net><epfafl$dpv$1@smc.vnet.net>
Hi David,
Thanks a ton.. that works excellently...
Ashesh
On Jan 27, 3:45 pm, "David W. Cantrell" <DWCantr... at sigmaxi.net>
wrote:
> "ashesh" <ashesh... at gmail.com> wrote:
> > Hi all,
>
> > I am trying to do the following two integrations, which are basically
> > the same, but with a change of variable. I am getting different results
> > from both of them. Hope some one can point out the mistake I am making.
>
> > a = 19.0; b = 4.0; t = 5.0;
>
> > Integrate[(a + b)/Sqrt[(a^2 - x^2)*(b^2 - x^2)], {x, b, b + I*t}]
>
> > Integrate[(1 + b/a)/Sqrt[(1 - y^2)*(1 - (b^2*y^2)/a^2)], {y, 1, (b +
> > I*t)/b}]
>
> > where y = (x/b)
>
> > The first integration gives: -1.23787 + 1.44831 I
>
> > while the second one gives: 6.17818 - 5.4757 I
>
> > The upper limits of the integrations are complex (b + i t) and ((b + i
> > t)/b) respectively.
>
> > The result from the first integration is correct and I have verified it
> > analytically.I suggest that you avoid using inexact numbers for a, b and t. The integral
> is unstable at its lower limit. (In fact, it mught be luck that your first
> integral gave the correct numerical answer.)
>
> For your second integration, I recommend
>
> In[9]:= a = 19; b = 4; t = 5;
> NIntegrate[(1 + b/a)/Sqrt[(1 - y^2)*(1 - (b^2*y^2)/a^2)], {y, 1, (b + I*t)/b}]
>
> Out[9]= -1.23787 + 1.44831 I
>
> David
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