Re: Different results for same integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg72991] Re: Different results for same integration*From*: "David W. Cantrell" <DWCantrell at sigmaxi.net>*Date*: Sat, 27 Jan 2007 06:53:51 -0500 (EST)*References*: <epcoj2$8gh$1@smc.vnet.net>

"ashesh" <ashesh.cb 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