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MathGroup Archive 2007

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Re: Different results for same integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72980] Re: Different results for same integration
  • From: "Sem" <sarner2006-sem at yahoo.it>
  • Date: Sat, 27 Jan 2007 06:09:43 -0500 (EST)
  • References: <epcoj2$8gh$1@smc.vnet.net>

"ashesh" <ashesh.cb at gmail.com> wrote news:epcoj2$8gh$1 at smc.vnet.net...
> 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.
>
> Looking forward for any help in resolving the problem.
>
> Ashesh
>

At first sight,
I think that you have too quickly simplified a complex-integral in a hybrid 
real-complex integral!


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