Question Number 19615 by icyfalcon999 last updated on 13/Aug/17 Answered by Tinkutara last updated on 13/Aug/17 $$\frac{\mathrm{1}}{\mathrm{4}}\underset{−\infty} {\overset{\infty} {\int}}\frac{{dx}}{{x}^{\mathrm{2}} \:+\:\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} }\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left[\mathrm{tan}^{−\mathrm{1}} \:\mathrm{2}{x}\right]_{−\infty} ^{\infty} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\left[\frac{\pi}{\mathrm{2}}\:−\:\left(−\frac{\pi}{\mathrm{2}}\right)\right]\:=\:\frac{\pi}{\mathrm{2}}…
Question Number 150684 by mathdanisur last updated on 14/Aug/21 $$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c};\mathrm{d}\in\mathbb{Z} \\ $$$$\left(\mathrm{b}-\mathrm{a}\right)\left(\mathrm{c}-\mathrm{a}\right)\left(\mathrm{d}-\mathrm{a}\right)\left(\mathrm{c}-\mathrm{b}\right)\left(\mathrm{d}-\mathrm{b}\right)\left(\mathrm{d}-\mathrm{c}\right) \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{is}\:\mathrm{divide} \\ $$$$\mathrm{into}\:\mathrm{12} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 85148 by M±th+et£s last updated on 19/Mar/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}+{x}^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{3}} +{x}^{\mathrm{7}} }\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 85146 by john santu last updated on 19/Mar/20 $$\mathrm{find}\:\mathrm{minimum}\:\&\:\mathrm{maximum}\:\mathrm{value}\: \\ $$$$\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\:−\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:\mathrm{x}−\frac{\mathrm{1}}{\mathrm{2}}\:,\:−\pi\leqslant\mathrm{x}\leqslant\pi \\ $$ Commented by mr W last updated on…
Question Number 19610 by ajfour last updated on 13/Aug/17 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle} \\ $$$$\mathrm{passing}\:\mathrm{through}\:\mathrm{the}\:\mathrm{midpoints} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{ABC}\:\mathrm{is} \\ $$$$\mathrm{half}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{circum}- \\ $$$$\mathrm{scribed}\:\mathrm{about}\:\mathrm{the}\:\mathrm{triangle}. \\ $$ Commented by ajfour last updated…
Question Number 150683 by Jonathanwaweh last updated on 14/Aug/21 Commented by Tawa11 last updated on 14/Aug/21 $$\mathrm{Great} \\ $$ Answered by ajfour last updated on…
Question Number 19609 by ajfour last updated on 13/Aug/17 Answered by ajfour last updated on 13/Aug/17 $$\mathrm{Equation}\:\mathrm{of}\:\mathrm{L}_{\mathrm{1}} : \\ $$$$\:\:\:\:\:\:\bar {\mathrm{z}}_{\mathrm{1}} \mathrm{z}+\mathrm{z}_{\mathrm{1}} \bar {\mathrm{z}}−\mathrm{2}\mid\mathrm{z}_{\mathrm{1}} \mid^{\mathrm{2}}…
Question Number 85142 by M±th+et£s last updated on 19/Mar/20 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{{n}} \left[{x}^{\mathrm{2}} \right]{dx}\:={n}\left({n}^{\mathrm{2}} −\mathrm{1}\right)−\underset{{k}=\mathrm{1}} {\overset{{n}^{\mathrm{2}} −\mathrm{1}} {\sum}}\sqrt{{k}}\: \\ $$ Answered by mind is…
Question Number 150678 by krauss last updated on 14/Aug/21 $$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\mathrm{3}−{x}^{\mathrm{2}} } \left(\mathrm{3}−{x}^{\mathrm{2}} −{y}\right){dy}\:{dx} \\ $$ Answered by Ar Brandon last…
Question Number 19604 by ajfour last updated on 13/Aug/17 Commented by ajfour last updated on 13/Aug/17 $$\mathrm{solution}\:\mathrm{to}\:\mathrm{Q}.\mathrm{19508} \\ $$$$\mathrm{To}\:\mathrm{prove}\:\mathrm{p}=\mid\mathrm{z}_{\mathrm{1}} −\mathrm{z}_{\mathrm{0}} \mid=\mid\frac{\bar {\alpha}\mathrm{z}_{\mathrm{1}} +\alpha\bar {\mathrm{z}}_{\mathrm{1}} +\mathrm{2c}}{\mathrm{2}\mid\alpha\mid}\mid…