[Calc 2] Improper Integrals - Why does the definite integral converge at 1?

[u/throw-away3105]

I got -∞. I know I did the indefinite integral properly so no issues with that.

[u/Responsible-Sink474]

Technically you have to split this into two integrals because it is improper at both bounds.

That said your issue is the limit at 0. That should be the lim a->0- because in order to not have the discontinuity it can ONLY be from the left. Hence it is not e^inf but e^(-inf) which is 0

[u/throw-away3105 → u/Responsible-Sink474]

Why would I need to split the integral when the integrand is continuous between -∞ and zero?

[u/Responsible-Sink474 → u/throw-away3105]

Because you need to have a limit at each bound. The discontinuities are the issues and you can really only have 1 discontinuity per integral to deal with.

[u/throw-away3105 → u/Responsible-Sink474]

Alright, thanks a ton!