## Integration, results are different in Mathematica 8 vs. Mathematica 11

1

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.

Question was closed 2017-03-19T15:48:08.403

2There 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. – Artes – 2017-03-16T09:04:26.807

2Comparing with NIntegrate, it appears the V8.0.4 expression above is inaccurate. – Michael E2 – 2017-03-16T10:26:59.770

1Note 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. – Michael E2 – 2017-03-19T13:57:32.563