1
$\begingroup$

I'm experiencing different results when integrating the following part of a code:

$Assumptions = {T > 298, P > 0};
ktccx = 70 - 0.01*(T - 298.15);
Vcc = (1 - 4*P/(4*P + ktccx))^(1/4);
dLGcc = Integrate[Vcc, {P, 0, P}]

Mathematica 8.0.4 returns:

ConditionalExpression[
     1.33333 (-0.25 + 
        0.707107 ((18.2454 + P - 0.0025 T)/(72.9815 - 0.01 T))^(
         3/4)) (72.9815 - 0.01 T),   P - 0.0025 T < -18.2454 || T <= 7298.15]

Mathematica 11.0.1 returns:

ConditionalExpression[(-0.00333333 + 6.16298*10^-35 I) (-1. + 
    1. (((7298.15 - 
         3.02923*10^-28 I) + (400. - 4.89859*10^-14 I) P - (1. - 
          4.93038*10^-32 I) T)/(7298.15 - 1. T))^(3/4)) (-7298.15 + 
    1. T), P - 0.0025 T <= -18.2454 || T <= 7298.15]

The latter shows Complex numbers and rest of the code crashes when dealing with variable dLGcc. Why this occurs? Any hint on this issue? The goal is to use the same code on Mathematica ver. 11, and get rid of the imaginary part.

Improve this question
$\endgroup$
3
  • 2
    $\begingroup$ There is no problem if you work with exact numbers instead of approximate ones, e.g.: Integrate[(1 - 4 s/(4 s + (70 - 1/100 (T - 29815/100))))^(1/4), {s, 0, P}, Assumptions -> T > 298 && P > 0]. One can work with ConditionalExpression seamlessly, nevertheless if one needs there is Normal, otherwise one should choose more specific assumptions. $\endgroup$
    – Artes
    Commented Mar 16, 2017 at 9:04
  • 2
    $\begingroup$ Comparing with NIntegrate, it appears the V8.0.4 expression above is inaccurate. $\endgroup$
    – Michael E2
    Commented Mar 16, 2017 at 10:26
  • 1
    $\begingroup$ Note that symbolic/exact solvers such as Integrate use algorithms that are not always numerically well-conditioned. I think that might be the source of the inaccuracy I mentioned. In any case it is usually better to use exact numbers with such solvers, as Artes suggested. $\endgroup$
    – Michael E2
    Commented Mar 19, 2017 at 13:57

0

Reset to default