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Question-168665

Question Number 168665 by mokys last updated on 15/Apr/22 Commented by cortano1 last updated on 15/Apr/22 $$\:{A}_{\mathrm{1}} =\:\underset{−\mathrm{2}} {\overset{\mathrm{0}} {\int}}\left(\mathrm{8}−{x}^{\mathrm{3}} \right){dx}=\:\left[\mathrm{8}{x}−\frac{{x}^{\mathrm{4}} }{\mathrm{4}}\right]_{−\mathrm{2}} ^{\mathrm{0}} \\ $$$$\:\:\:\:\:\:=\:\mathrm{8}\left(\mathrm{2}\right)−\frac{\mathrm{1}}{\mathrm{4}}\left(−\mathrm{16}\right)=\mathrm{16}+\mathrm{4}=\mathrm{20}…

if-the-circle-x-2-y-2-2y-8-0-and-x-2-y-2-24x-hy-0-cut-orthogonally-determine-the-value-of-h-

Question Number 37591 by mondodotto@gmail.com last updated on 15/Jun/18 $$\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{circle}}\:\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{y}}−\mathrm{8}=\mathrm{0} \\ $$$$\boldsymbol{\mathrm{and}}\:\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} −\mathrm{24}\boldsymbol{{x}}+\boldsymbol{{hy}}=\mathrm{0}\:\boldsymbol{\mathrm{cut}}\:\boldsymbol{\mathrm{orthogonally}}, \\ $$$$\boldsymbol{\mathrm{determine}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{{h}}. \\ $$$$ \\ $$ Answered by tanmay.chaudhury50@gmail.com…

Li-z-2-z-1-ln-t-dt-Li-a-ib-R-2-a-ib-1-ln-t-dt-iI-2-a-ib-1-ln-t-dt-Can-you-explain-me-how-get-the-formula-for-R-Li-z-and-I-Li-z-

Question Number 103124 by Faetma last updated on 12/Jul/20 $$\mathrm{Li}\left({z}\right)=\int_{\mathrm{2}} ^{{z}} \frac{\mathrm{1}}{\mathrm{ln}\:{t}}\mathrm{d}{t} \\ $$$$\mathrm{Li}\left({a}+{ib}\right)=\mathfrak{R}\left(\int_{\mathrm{2}} ^{{a}+{ib}} \frac{\mathrm{1}}{\mathrm{ln}\:{t}}\mathrm{d}{t}\right)+{i}\mathfrak{I}\left(\int_{\mathrm{2}} ^{{a}+{ib}} \frac{\mathrm{1}}{\mathrm{ln}\:{t}}\mathrm{d}{t}\right) \\ $$$$\mathrm{Can}\:\mathrm{you}\:\mathrm{explain}\:\mathrm{me} \\ $$$$\mathrm{how}\:\mathrm{get}\:\mathrm{the}\:\mathrm{formula} \\ $$$$\mathrm{for}\:\mathfrak{R}\left(\mathrm{Li}\left({z}\right)\right)\:\mathrm{and} \\…

I-want-to-write-0-a-ib-f-x-dx-but-with-the-form-i-How-write-that-Sorry-for-my-bad-english-

Question Number 103073 by Faetma last updated on 12/Jul/20 $$\mathrm{I}\:\mathrm{want}\:\mathrm{to}\:\mathrm{write} \\ $$$$\int_{\mathrm{0}} ^{{a}+{ib}} {f}\left({x}\right)\mathrm{d}{x} \\ $$$$\mathrm{but}\:\mathrm{with}\:\mathrm{the}\:\mathrm{form} \\ $$$$\alpha+{i}\beta \\ $$$$\mathrm{How}\:\mathrm{write}\:\mathrm{that}? \\ $$$$\mathrm{Sorry}\:\mathrm{for}\:\mathrm{my}\:\mathrm{bad} \\ $$$$\mathrm{english} \\…