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So, I'm new to Mathematica. I tried evaluating the following definite integral. However the answer i get from wolfram alpha & mathematica are different. Can someone please point out what I'm missing? The answer from wolframAlpha is correct according to Casio fx-991-es 

Integrate[1/(1 + t) ((t + 0.8)/(t + 1))^20, {t, -0.8, 0}]

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  • $\begingroup$ Please paste copy&pastable code instead of screenshots. It is not fair to the people who are trying to assist to make them need to retype all your content based on some images. $\endgroup$
    – ktm
    Commented Sep 9, 2018 at 1:43
  • $\begingroup$ oh I'm sorry Integrate[1/(1 + t) ((t + 0.8)/(t + 1))^20, {t, -0.8, 0}] $\endgroup$
    – Ramith Hettiarachchi
    Commented Sep 9, 2018 at 1:45

1 Answer 1

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Precision issues. Use one of the following instead.

Symbolic integration:

Integrate[(1/(1 + t)) ((t + 4/5)/(t + 1))^20, {t, -4/5, 0}]
(*-(318650448087859023644/198221683502197265625) + Log[5]*)

N@%
(*0.00189205*)

Numeric integration with a higher working precision:

NIntegrate[(1/(1 + t)) ((t + .8`20)/(t + 1))^20, {t, -.8`20, 0}]
(*0.00189205*)
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  • $\begingroup$ Usually when do these issues occur? should i use NIntegrate instead? $\endgroup$
    – Ramith Hettiarachchi
    Commented Sep 9, 2018 at 1:52
  • $\begingroup$ These issues appear when machine precision numbers are insufficient for the precision needed to accurately compute what you require. $\endgroup$
    – ktm
    Commented Sep 9, 2018 at 1:54
  • $\begingroup$ There's a ton of doc pages on these topics. Here's another useful one: Control the Precision and Accuracy of Numerical Results $\endgroup$
    – ktm
    Commented Sep 9, 2018 at 1:55
  • $\begingroup$ Appreciate your help 🙌Thanks! $\endgroup$
    – Ramith Hettiarachchi
    Commented Sep 9, 2018 at 1:57
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    $\begingroup$ @RamithHettiarachchi -- (1) Note further that if you do just add an N in front of your Integrate[..], you get the same answer as the NIntegrate[..] in this post. Higher precision is unnecessary in the numerical integrator. (2) Symbolic solvers such as Integrate often have trouble with "inexact" floating-point input. (3) Interesting aside: Integrate[(1/(1 + t)) ((t + .8`20)/(t + 1))^20, {t, -.8`20, 0}] caused my kernel to crash! So even with high-precision approximate inputs, exact solvers may still have problems. $\endgroup$
    – Michael E2
    Commented Sep 9, 2018 at 19:02

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