TI-89 Titanium INTEGRATION Flaw?

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Discussion Overview

The discussion revolves around a perceived flaw in the TI-89 Titanium calculator's integration output for the integral of the function 1/[G-(Cv)/M] with respect to "v". Participants explore the differences between the user's expected result and the calculator's output, focusing on the implications of constants of integration and the properties of logarithms.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • The user, SWITCH, believes the correct integral is -(M/C)[ln(G-(Cv)/M)], while the TI-89 returns -(M/C)[ln(|Cv-GM|)].
  • One participant suggests that the difference between the two answers is merely a constant of integration, which is often omitted in integration results.
  • Another participant questions the necessity of removing the fraction in the denominator, seeking clarification on the reasoning behind it.
  • A different participant asserts that both answers are incorrect as they lack the constant of integration.
  • One contributor argues that the calculator's answer is generally correct because it includes the absolute value in the logarithm, which is a standard mathematical practice.
  • Another participant references a specific integral form, suggesting that understanding this could help resolve the user's confusion without relying on the calculator.
  • A later reply encourages the user to apply logarithmic properties to reconcile the two answers, implying they are equivalent under certain conditions.

Areas of Agreement / Disagreement

Participants express differing views on the correctness of the answers provided by the user and the calculator. There is no consensus on which answer is definitively correct, as the discussion highlights multiple interpretations and approaches to the integration problem.

Contextual Notes

Participants note that both answers are missing the constant of integration, which is a critical aspect of indefinite integrals. The discussion also emphasizes the importance of absolute values in logarithmic functions, which may affect the interpretation of the results.

Switch_fx
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TI-89 Titanium INTEGRATION Flaw?

Ok so this is my first post, and I am in dire need of assistance. I have a big exam tomorrow and if I can't figure out why my TI-89 is screwing up this simple integration I am in some trouble...

I am looking for the integral of : 1/[G-(Cv)/M] with respect to "v"

(erroneus, G=gravitational constant, C=drag coefficient, M=mass, and V=velocity)

anyways...
I know the correct answer is : -(M/C)[ln(G-(Cv)/M)]

but my TI-89 calculator gives back the answer as:

-(M/C)[ln(|Cv-GM|)]

If anyone could please explain to me why this is so or what I am doing wrong it would be of great help...and yes I am inputting the integral in the correct fashion

Thanks to anyone who can help!


~SWITCH
 
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If you get rid of the fraction in the denominator in the original function you will arrive at the answe your calculator does, however you should notice that these only differ by a constant and that when you integrate you always have to add on a constant of integration.
 
Why would I get rid of the fraction in the denominator? And if I get rid of it what do I replace it with?
 
You asked a question, you got an answer. Read the answer again. By the way, neither your answer nor the calculator's answer is correct!

Both are missing the added constant. d_leet's point is that your and the calculator's answer differ only by a constant.
 
If we leave the constant part, the calculator is right in general, as it gives the absolute value of quantity inside logarithm.
 
Last edited:
Maybe if it's hard for you to integrate 1/(1-ax) with respect to x then you do have a problem?

Taken from 1/a onwards, the integral of 1/1-ax is (-1/a) ln |1-ax|. Knowing how that solve your problem without needing the calculator.
 
Switch_fx said:
Ok so this is my first post, and I am in dire need of assistance. I have a big exam tomorrow and if I can't figure out why my TI-89 is screwing up this simple integration I am in some trouble...

I am looking for the integral of : 1/[G-(Cv)/M] with respect to "v"

(erroneus, G=gravitational constant, C=drag coefficient, M=mass, and V=velocity)

anyways...
I know the correct answer is : -(M/C)[ln(G-(Cv)/M)]

but my TI-89 calculator gives back the answer as:

-(M/C)[ln(|Cv-GM|)]

If anyone could please explain to me why this is so or what I am doing wrong it would be of great help...and yes I am inputting the integral in the correct fashion

Thanks to anyone who can help!


~SWITCH

Take the "correct" answer, and use the logarithmic rule for division: ln(a/b) = ln(a) - ln(b). Normally I'd get in trouble for telling you that, but you could have just as easily looked it up in the textbook, so I thought I'd save you a couple minutes of tedious page turning. Anyway, considering what the others here have told you, just by expanding your answer in this way, you should be convinced that your answer and the 89's answer are the same.
 

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