Question

Is WolframAlpha correct?

http://www.wolframalpha.com/input/?i=definite+integral&a=*C.definite+integral-_*Calculator.dflt-&f2=1%2Fx&f=DefiniteIntegralCalculator.integrand_1%2Fx&f3=x&f=DefiniteIntegralCalculator.variable%5Cu005fx&f4=0&f=DefiniteIntegralCalculator.rangestart%5Cu005f0&f5=0&f=DefiniteIntegralCalculator.rangeend_0

Answer 1

I'm confused because 1/x doesn't exist at x=0.

Answer 2

So I think it is supposed to be undefined.

Answer 3

So strange. I think it's using the property

\[\Large \int_{k}^{k}f(x) = 0\]

but the issue is like you pointed out: 0 isn't in the domain of f(x) = 1/x

Answer 4

So it IS supposed to be undefined?

Answer 5

Just checking.

Answer 6

I think so

Answer 7

What do you think? @phi

Answer 8

I would look up improper integral
https://en.wikipedia.org/wiki/Improper_integral

Answer 9

and interpret it to mean
\[ \lim_{a \rightarrow 0^+} \int_a^{a} \frac{dx}{x} \]

Answer 10

Okay, I get it. Thanks!

Answer 11

What did you conclude?

Note: Software has to make choices. There is no substitute for a knowledgeable user.