Can Wolfram Mathematica be wrong on this Integration?

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Homework Help Overview

The discussion revolves around the use of Wolfram Mathematica for evaluating an integral, with the original poster questioning the accuracy of the software's output compared to other methods, including Symbolab and manual calculations.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the discrepancies between Mathematica's results and those from other tools, questioning the steps taken in the calculations and the definitions used. There are attempts to replicate the integral with different variable definitions and numerical inputs to understand the behavior of the software.

Discussion Status

Some participants have provided insights into potential quirks of Mathematica, suggesting alternative approaches like using NIntegrate and redefining variables to achieve different results. The conversation reflects a mix of experiences and opinions regarding the reliability of Mathematica for integral calculations.

Contextual Notes

There is mention of the original poster's beginner status with Mathematica, raising concerns about whether to trust the software for integral evaluations or rely on manual methods. The discussion also touches on the internal representation of numbers in Mathematica and its impact on calculations.

srecko97
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Homework Statement


Mathematica vs (Symbolab + my brain)

Homework Equations

The Attempt at a Solution


I think this integral calculation in Mathematica is wrong. Open pictures below.
Please help me.

Graphs (the red one is under the blue and the green):
bACa3G

https://ibb.co/bACa3G
Wolfram Mathematica
iREcHb

https://ibb.co/iREcHb
Symbolab:
jHhKVw

https://ibb.co/jHhKVw
 
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You've shown us steps 21, 23, 24 and then jumped to step 30. What happened in between those two? Mathematica remembers any definitions that might have been made between those two. If you restart the kernel and do just those steps you've shown, does it get the same answer?
 
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I have deleted everything between 24 and 30. I also tried to solve it in another notebook. I inserted numbers inside the integral instead of pre-defined variables. The results were always 0. Try to retype the same integral in Mathematica please. I am quite sure that you will get 0 too
 
It seems you've run into a weird quirk/bug in how Mathematica integrates. I found if you define ##\alpha=3912023/100000## and ##\beta = 103/100## and use ##\beta X## as the lower limit of the integral, you get the correct non-zero answer. Also, if you use NIntegrate instead of Integrate, you'll also get the correct answer.
 
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Thanks. I am a beginner user of Wolfram Mathematica. Do you have a lot of such problems with Mathematica? Should I trust it or it is better to solve integrals on paper?
 
Mathematica is a powerful tool, but you don't want to trust it blindly. Just like when you do calculations on paper, you still need to check if the results you get make sense. I'm not exactly sure what's going on in this case, but it seems to have to do with how Mathematica represents numbers internally. For example, if you type in "100-100/3*3" and "b=100-100.0/3*3" into Mathematica, you get different results because in the first case, the software represents 100/3 internally as a fraction, but in the second case, it represents 100.0/3 as a floating-point number, which has limited accuracy by its nature.
 
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Thank you vela!
 
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