- #1
Sara991
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How do I solve this integral?
<br /> \int \frac{1}{dx}<br />
<br /> \int \frac{1}{dx}<br />
What Is the Correct Approach to Solving \(\int \frac{1}{dx}\)?
- Thread starter Sara991
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SUMMARY
The integral \(\int \frac{1}{dx}\) is fundamentally nonsensical and cannot be solved. Participants in the discussion clarified that the correct expression should be \(\int \frac{1}{x}\,dx\). The integral \(\int dx\) represents the sum of infinitesimally small quantities, while \(\frac{1}{dx}\) implies an uncountably large quantity, leading to confusion. The thread concluded with a consensus that without proper context or a complete problem statement, further explanation is futile.
PREREQUISITES- Understanding of integral calculus
- Familiarity with the notation of differentials (dx)
- Knowledge of the properties of limits and infinitesimals
- Basic skills in mathematical problem formulation
- Study the correct formulation of integrals, focusing on \(\int \frac{1}{x}\,dx\)
- Learn about the concept of differentials and their role in calculus
- Explore the implications of infinitesimals in calculus
- Review common mistakes in integral calculus to avoid confusion
Students of calculus, mathematics educators, and anyone seeking to clarify misconceptions in integral notation and its applications.
- #2
vela
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You can't. Did you by chance mean
\int \frac{1}{x}\,dx
\int \frac{1}{x}\,dx
- #3
Sara991
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Hi dear
I mean:
<br /> \int \frac{1}{dx}<br />
I mean:
<br /> \int \frac{1}{dx}<br />
- #4
vela
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That expression doesn't make sense. Where did it come from?
- #5
Sara991
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I encounter with this, when I am solving a problem.
- #6
HallsofIvy
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Then please give the entire problem. As vela said,
\int \frac{1}{dx}
simply doesn't mean anything.
\int \frac{1}{dx}
simply doesn't mean anything.
- #7
Sara991
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So Sorry, I am not able to explain it.
- #8
Char. Limit
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Well, since \int dx[/tex] means a sum (\int) of an uncountably large amount of infinitesimally small numbers (dx's)...<br />
<br />
and since, if dx is infinitesimally small, 1/dx would be uncountably large...<br />
<br />
Then \int \frac{1}{dx} means a sum of an uncountably large amount of uncountably large numbers...<br />
<br />
and so is uncountably large itself.
- #9
Hurkyl
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Ugh, first the opening poster won't go into where she got the expression so we can point out what she did wrong, but now people are giving her questionable advice. 
Thread closed.
Thread closed.