Ask Uncle Colin: An Undefined Integral | Colin

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can.

Dear Uncle Colin,

I have a disagreement with my teacher about the integral $\int_{-1}^{1} x^{-1} \dx$. I understand you have to split the integral into two parts, which I’m happy with. They split it from -1 to $a$, letting $a \rightarrow 0_-$ and from $b$ to 1, letting $b \rightarrow 0_+$; both of those integrals diverge, so the answer is…

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