Natural log fxn = negative integral?

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SUMMARY

The statement ln(1/10) = -∫ dx/x is false without specified limits of integration. The integral -∫ dx/x requires limits to evaluate correctly, specifically -∫_1^{10} (1/x) dx, which accurately represents the natural logarithm of 1/10. The discussion clarifies that the absence of limits leads to confusion regarding the validity of the equation.

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  • Familiarity with integration techniques, specifically for 1/x
  • Basic calculus concepts, including limits of integration
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Jules18
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Homework Statement


True or false?

ln(1/10) = -\int dx/x

The Attempt at a Solution



I have no idea where to start on this one.

what is dx/x ??
 
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right side means that u are supposed to integrate with respect to x

-Integrate[1/x] with respect to x
 
This is obviously not true as posted. Are there limits of integration that we're not seeing?
I.e., does the integral look like this?
-\int_1^{10} \frac{dx}{x}
 
ok I get it. the limits are missing, it must be a typo, but otherwise this makes sense to me now thanks
 

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