Question Number 87862 by Rio Michael last updated on 06/Apr/20
$$\mathrm{Evaluate}\:\:\:\:\overset{\mathrm{1}} {\int}_{−\mathrm{1}} \frac{\mathrm{1}}{{x}−\mathrm{1}}\:{dx}\: \\ $$
Commented by MJS last updated on 06/Apr/20
$$\mathrm{doesn}'\mathrm{t}\:\mathrm{exist} \\ $$$$\int\frac{{dx}}{{x}−\mathrm{1}}=\mathrm{ln}\:\mid{x}−\mathrm{1}\mid\:+{C} \\ $$$$\mathrm{but}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\mathrm{ln}\:\mid{x}−\mathrm{1}\mid\:=−\infty \\ $$
Commented by Rio Michael last updated on 06/Apr/20
$$\mathrm{so}\:\mathrm{sir}\:\mathrm{can}\:\mathrm{we}\:\mathrm{say}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{diverges}? \\ $$
Commented by MJS last updated on 07/Apr/20
$$\mathrm{yes} \\ $$