Re: Different results for same integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg72973] Re: [mg72964] Different results for same integration*From*: leigh pascoe <leigh at cephb.fr>*Date*: Sat, 27 Jan 2007 05:41:38 -0500 (EST)*References*: <200701261242.HAA10459@smc.vnet.net>

ashesh 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. > > Looking forward for any help in resolving the problem. > > Ashesh > > > > It helps to do these symbolically first a = 19; b = 4; t = 5; Integrate[(a + b)/Sqrt[(a^2 - x^2)*(b^2 - x^2)], {x, b, b + I*t}] Out: \!\(â?«\_4\%\(4 + 5\ \[ImaginaryI]\)\(23\/\@\(\((16 - x\^2)\)\ \((361 - x\^2)\)\)\) \[DifferentialD]x\) x = b*y; Integrate[(1 + b/a)/Sqrt[(1 - y^2)*(1 - (b^2*y^2)/a^2)], {y, 1, (b + I*t)/b}] Out: \!\(â?«\_1\%\(1 + \(5\ \[ImaginaryI]\)\/4\)\(23\/\(19\ \@\(\((1 - y\^2)\)\ \((1 \ - \(16\ y\^2\)\/361)\)\)\)\) \[DifferentialD]y\) I can't get Ma to do this for me, but if you take the second expression and put y=4x and dy=4dx, you get the integral of 23/â??(16-x^2)(361-16x^2) whereas the first expression evaluates to the integral of 23/â??(16-x^2)(361-x^2) So these don't seem to be equivalent expressions. Leigh

**References**:**Different results for same integration***From:*"ashesh" <ashesh.cb@gmail.com>