Integration Sign Error: TI-Nspire Solution

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Discussion Overview

The discussion revolves around an integration sign error encountered while using a TI-Nspire calculator. Participants are examining the source of a negative sign in the output and debating the correctness of the resulting expression, including its implications for real logarithms.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions the origin of a negative sign in the calculator's output and suggests that substitution may not be necessary for solving the problem.
  • Another participant argues that the negative sign should actually be a positive sign, asserting that the other answer is incorrect because it leads to a negative logarithm, which is not valid for real numbers.
  • A different participant reflects on their misunderstanding, indicating that the calculator's output can be simplified to a different form that avoids the negative sign.
  • One participant comments on the misuse of the implication sign in mathematical expressions, suggesting that it is often incorrectly applied in contexts where it does not make sense.

Areas of Agreement / Disagreement

Participants express differing views on the correctness of the negative sign in the output, with some agreeing on the need for a positive sign while others remain uncertain about the implications of the expressions involved. The discussion does not reach a consensus.

Contextual Notes

There are unresolved issues regarding the assumptions made in the calculations and the definitions of the expressions involved, particularly concerning the validity of logarithms of negative values.

karush
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View attachment 2106

the bk did not give an answer for this but my TI-nspire gave what is shown,
however I don't know where the - sign (see red arrow) comes from. I looked at the steps given in W|A but thot all the substitution was not needed to solve this.
 
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I agree with you. The $-$ sign should be a $+$. You can tell that the other answer is wrong, because $-\cos x - 1$ is negative and so will not even have a real logarithm.
 
ok think I see where I was blind on this

the calculator gave
$\displaystyle
\ln{\left(-\left(\cos{x}-1\right)\right))}
$
which if you distribute the $$-1$$
then $$\ln\left(-\cos(x)+1\right)$$
would be the answer
 
The misuse of the $\implies$ sign is common and makes no sense when writing things like $1+1\implies2.$ It's used when you already stated an equality and want to "imply" some consequence.
 

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