- #1

Saracen Rue

- 150

- 10

- TL;DR Summary
- Why is ##\int_{-1}^{1} \frac {1} {x} dx## undefined?

I've always been taught that the indefinite integral of ##\frac{1}{x}## is ##\ln(|x|)##. Extending this to definite integrals, particularly over limits involving negative values, should work just like any other integral:

$$\int_{-1}^{1} \frac {1} {x} dx = \ln(|-1|) - \ln(|1|) = \ln(1) - \ln(1) = 0 - 0 = 0$$

However, this doesn't seem to be the case as every online calculator/program I use states the answer as being undefined. What I'm struggling with is

Thank you for your time.

$$\int_{-1}^{1} \frac {1} {x} dx = \ln(|-1|) - \ln(|1|) = \ln(1) - \ln(1) = 0 - 0 = 0$$

However, this doesn't seem to be the case as every online calculator/program I use states the answer as being undefined. What I'm struggling with is

*why*it's undefined, as all the rules I know for integration and maths in general imply the answer should be ##0##. I should note that I've never been the strongest with understanding the theory behind a lot of calculus. My teachers always dismissed my questions in high school or didn't know the answers themselves and insisted for me to just follow the formulae they give to get the answers they want. Any actual theory I know is self taught, so I apologies in advance if I struggle to follow explanations for this question if cover more complicated theory.Thank you for your time.