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MathGroup Archive 2007

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Different results for same integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72964] Different results for same integration
  • From: "ashesh" <ashesh.cb at gmail.com>
  • Date: Fri, 26 Jan 2007 07:42:42 -0500 (EST)

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


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