- #1

Hepth

Gold Member

- 464

- 40

Code:

```
$Assumptions = 0 < u <= 19/80 && I10 \[Element] Reals;
FXN = Sqrt[(u - 15/16)^2 - 2/5 (u + 17/16) + 1/25] (I10 (u^2) - 1/u);
PA = Integrate[FXN /. {I10 -> 1/2 Log[1/2]}, u];
PB = Integrate[FXN, u] /. {I10 -> 1/2 Log[1/2]};
Plot[{Re[PA], Re[PB]}, {u, 0, 0.243}]
PA = Integrate[FXN /. {I10 -> 0.5 Log[1/2]}, u];
PB = Integrate[FXN, u] /. {I10 -> 0.5 Log[1/2]};
Plot[{Re[PA], Re[PB]}, {u, 0, 0.243}]
```

What I am doing is finding the upper limit of an integral. If I make a replacement of a variable to a constant before or after the integration I get different results. The constant is not complex, and is a real number, though contains a Log[1/2].

I know the Sqrt in FXN is only real for u<0.243 ish, and my limit of integration is right below that.

I have tried limits too, and its the same as just a replacement rule.

NOTICE, if you change the 1/2 to 0.5 in the replacement rule it works.

Is there a way I can get these to be the same no matter what?