Question Number 136762 by snipers237 last updated on 25/Mar/21 $$\:{let}\:\:{C}\left({a},{r}\right)=\left\{{z}\in\mathbb{C},\:\:\mid{z}−{a}\mid={r}\:\right\} \\ $$$${Let}\:{u},{v},{w}\:\in{C}\left({a},{r}\right)\:{such}\:{as}\:\:\:{u}+{v}=\mathrm{2}{w} \\ $$$${Prove}\:{that}\:\:\frac{{u}−{a}}{{v}−{a}}\:=\mathrm{1}\:,\:{u}={v}={w} \\ $$$$ \\ $$$${It}\:{shows}\:{that}\:{the}\:{middle}\:{of}\:{a}\:{segment}\: \\ $$$${joining}\:{two}\:{points}\:{in}\:{a}\:{circle}\:\:{is}\:{not}\:{in}\:{that}\:{circle} \\ $$ Terms of Service…
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Question Number 136750 by mnjuly1970 last updated on 25/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:…..{advanced}\:\:\:\:{calculus}….. \\ $$$$\:\:\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:…\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}−{e}^{−{x}^{\mathrm{2}} } }{{x}^{\mathrm{2}} }{dx}=\sqrt{\pi}\:\:\:\: \\ $$ Answered by Ñï= last…
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Question Number 136723 by mnjuly1970 last updated on 25/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{calculus}\:\:\:\:\:\left({I}\right)….. \\ $$$$\:\:\:\:\:{prove}\:\:\:{that}\::: \\ $$$$\:\:\:\:{f}\left({x}\right)=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\mathrm{4}{x}}}\:\overset{???} {=}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\begin{pmatrix}{\:\mathrm{2}{n}}\\{\:\:\:{n}}\end{pmatrix}\:{x}^{{n}} \\ $$$$ \\ $$ Answered by Dwaipayan Shikari…
Question Number 71175 by 20190927 last updated on 12/Oct/19 $$\int\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{2016x}}\mathrm{dx} \\ $$ Commented by Prithwish sen last updated on 12/Oct/19 $$\int\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{1008}\right)^{\mathrm{2}} −\left(\mathrm{1008}\right)^{\mathrm{2}} }\:\:\:\:\:\:\boldsymbol{\mathrm{put}}\:\boldsymbol{\mathrm{x}}+\mathrm{1008}\:=\:\boldsymbol{\mathrm{t}} \\…
Question Number 5628 by sanusihammed last updated on 23/May/16 $${If}\:\:\:{siny}\:=\:{xsin}\left({a}\:+\:{y}\right) \\ $$$$ \\ $$$${Show}\:{that}\:\:\frac{{dy}}{{dx}}\:\:=\:\:\frac{{sin}^{\mathrm{2}} \left({a}\:+\:{y}\right)}{{sina}} \\ $$$$ \\ $$$$ \\ $$$${Please}\:{help}.\:{Thanks}\:{in}\:{advance}. \\ $$ Terms of…
Question Number 136680 by aupo14 last updated on 24/Mar/21 Answered by Olaf last updated on 24/Mar/21 $$\mathrm{F}\left({x}\right)\:=\:\int\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{9}\right)^{\mathrm{2}} } \\ $$$$\mathrm{Let}\:{x}\:=\:\mathrm{3sh}{u} \\ $$$$\mathrm{F}\left({u}\right)\:=\:\int\frac{\mathrm{3ch}{u}}{\left(\mathrm{9sh}^{\mathrm{2}} +\mathrm{9}\right)^{\mathrm{2}} }\:{du}…
Question Number 71142 by mathmax by abdo last updated on 12/Oct/19 $${find}\:\int\sqrt{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}{dx} \\ $$ Commented by MJS last updated on 12/Oct/19 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{we}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this} \\ $$ Terms…
Question Number 136651 by mhabs last updated on 24/Mar/21 Answered by Ñï= last updated on 24/Mar/21 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{\mathrm{1}}{\mathrm{1}+\left({a}\mathrm{tan}\:{x}\right)^{\mathrm{2}} }{dx}\overset{{t}=\mathrm{tan}\:{x}} {=}\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{\mathrm{1}+{a}^{\mathrm{2}} {t}^{\mathrm{2}} }\centerdot\frac{\mathrm{1}}{\mathrm{1}+{t}^{\mathrm{2}}…