The attached worksheet describes the issue.
The numerical integrated value does not match the values in the plotted graphic over the same range.
I am likely making a novice mistake, but any help would be appreciated.
You are absolutely correct! See, I told you I probably did something stupid.
Thanks for your help. I get in a hurry and skip steps I know not to skip.
You may have forgotten to subtract the value of f1 at b=0:
Clear[f1]; f1[b_] = Integrate[(b Sqrt[1 - b^2])/(1 - b)^2, b]; ListPlot[Table[f1[b], {b, 0, .13, .01}]] ListPlot[Table[f1[b] - f1[0], {b, 0, .13, .01}]]
Not sure what you are repling to.
If I integrate my expression, I get an analytical function that has a value of 3 when the variable goes to zero, but the ListPlotTable[NIntegrate]] for that same integrated function shows the correct value....0....when the variable goes to zero. The analytical function is biased upward by 3 units...and the curve that is generated is the same as the ListPlot only biased upward by 3 units.
My conclusion is that Mathematica has incorrectly performed the integration on the function and has given me an incorrect analytical expression. I can live with the numerical integration but the disconnect with the analytical expression was unexpected.
