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Category: Integration

nice-calculus-Evaluate-0-1-sin-ln-x-ln-x-ln-2-x-dx-Ans-ln-2-pi-4-1-

Question Number 126465 by mnjuly1970 last updated on 20/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:\mathscr{E}{valuate}\:… \\ $$$$\:\:\:\:\:\:\:\:\phi\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{sin}\left({ln}\left({x}\right)\right)−{ln}\left({x}\right)}{{ln}^{\mathrm{2}} \left({x}\right)}{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathscr{A}{ns}\:::\:{ln}\left(\sqrt{\mathrm{2}}\:\right)+\frac{\pi}{\mathrm{4}}\:−\mathrm{1}\:… \\ $$ Commented by talminator2856791 last…

lim-x-3-x-3-x-3-show-right-and-left-side-limit-

Question Number 126427 by Study last updated on 20/Dec/20 $${li}\underset{{x}\rightarrow−\mathrm{3}} {{m}}\frac{\mid{x}+\mathrm{3}\mid}{{x}+\mathrm{3}}\:\:\:\:\:\:{show}\:{right}\:{and}\:{left}\:{side} \\ $$$${limit}?? \\ $$ Answered by liberty last updated on 20/Dec/20 $$\underset{{x}\rightarrow−\mathrm{3}^{−} } {\mathrm{lim}}\left[\:\frac{\mid{x}+\mathrm{3}\mid}{{x}+\mathrm{3}}\:\right]\:=\:\underset{{x}\rightarrow−\mathrm{3}^{−}…

pi-pi-sin-1-1-x-2-dx-

Question Number 60881 by aliesam last updated on 26/May/19 $$\underset{−\pi} {\overset{\pi} {\int}}{sin}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}^{\mathrm{2}} }\right)\:{dx} \\ $$ Commented by MJS last updated on 26/May/19 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{we}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this},\:\mathrm{not}\:\mathrm{even} \\ $$$$\mathrm{approximate}.\:\mathrm{it}'\mathrm{s}\:\mathrm{undefined}\:\mathrm{at}\:{x}=\pm\mathrm{1}\:\mathrm{and}…