Question Number 115058 by mnjuly1970 last updated on 23/Sep/20 $$\:\:\:\:\:\:\:….\:\:{nice}\:\:{calculus}\:… \\ $$$$\:\:\:\:\:\:{a}\:,\:{b}\:,\:{c}\:,\:{d}\:\:\in\mathbb{N}\:{and}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}+\frac{\mathrm{1}}{{d}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{find}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{max}\left({a}+{b}+{c}+{d}\right)\:=??? \\ $$$$\:\:\:\:\:\:…{m}.{n}.{july}.\mathrm{1970}… \\ $$ Answered…
Question Number 115055 by mnjuly1970 last updated on 23/Sep/20 $$\:\:\:\:\:\:\:\:\:\:\:…\:\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:\:{evaluation}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\chi=\int_{\mathrm{0}} ^{\:\mathrm{1}} {log}\left(\mathrm{1}−{x}\right).{log}\left(\mathrm{1}+{x}\right)\:=??? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{m}.{n}.{july}.\mathrm{197}{o}… \\ $$$$\: \\ $$ Answered…
Question Number 115051 by gab last updated on 23/Sep/20 $$\int{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{2}} −\mathrm{2}}{dx} \\ $$ Commented by Dwaipayan Shikari last updated on 23/Sep/20 $$\int\mathrm{2}\sqrt{\mathrm{2}}{sin}^{\mathrm{2}} \theta{cos}\theta\sqrt{\mathrm{2}{sin}^{\mathrm{2}} \theta−\mathrm{2}}\:{d}\theta\:\:\:\:\:\:\:\:\:\:\:{x}=\sqrt{\mathrm{2}}{sin}\theta\:\Rightarrow\mathrm{1}=\sqrt{\mathrm{2}}\:{cos}\theta\frac{{d}\theta}{{dx}}\:…
Question Number 115030 by bobhans last updated on 23/Sep/20 $$\underset{−\frac{\pi}{\mathrm{2}}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\sqrt{\mathrm{sec}\:{x}−\mathrm{cos}\:{x}}\:{dx}\:=? \\ $$ Answered by bemath last updated on 23/Sep/20 $$\underset{−\frac{\pi}{\mathrm{2}}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\sqrt{\frac{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}}{\mathrm{cos}\:{x}}}\:{dx}\:=\:\underset{−\frac{\pi}{\mathrm{2}}}…
Question Number 115026 by jm2bok last updated on 23/Sep/20 $$\mathrm{Solve}:\:\:\int_{\mathrm{1}/\pi} ^{\mathrm{1}/\mathrm{2}} \mathrm{ln}\:\lfloor\frac{\mathrm{1}}{{x}}\rfloor{dx} \\ $$ Answered by PRITHWISH SEN 2 last updated on 23/Sep/20 $$\mathrm{when} \\…
Question Number 115009 by arcana last updated on 22/Sep/20 $$\int_{\mathrm{C}} \frac{{e}^{{z}} }{\mathrm{1}−\mathrm{cos}\:{z}}{dz}\:;\:\mathrm{C}:\mid{z}\mid=\mathrm{1} \\ $$ Answered by Olaf last updated on 24/Sep/20 $$ \\ $$$$\int_{\mathrm{C}} \frac{\mathrm{co}{z}+{i}\mathrm{sin}{z}}{\mathrm{1}−\mathrm{cos}{z}}{dz}…
Question Number 115000 by mnjuly1970 last updated on 22/Sep/20 $$\:\:\:\:\:\:\:\:\:\:\:\:….{nice}\:\:\:{math}… \\ $$$$ \\ $$$$\:{if}\:\:{y}\:=\left({cos}\left(\mathrm{2}{x}\right)\right)^{−\frac{\mathrm{1}}{\mathrm{2}}} \:{then} \\ $$$${prove}\:::\:\:\:{y}+{y}^{''} =\:\mathrm{3}{y}^{\mathrm{5}} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:…{m}.{n}.{july}.\mathrm{1970}… \\ $$ Answered…
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Question Number 180471 by universe last updated on 12/Nov/22 Commented by Sheshdevsahu last updated on 12/Nov/22 $$\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{i}}'\boldsymbol{\mathrm{m}}\:\boldsymbol{\mathrm{not}}\:\boldsymbol{\mathrm{wrong}},\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{similar}}\:\boldsymbol{\mathrm{type}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{question}}\:\boldsymbol{\mathrm{was}} \\ $$$$\boldsymbol{\mathrm{asked}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{jee}}\left(\boldsymbol{\mathrm{advanced}}\right)\:\left(\boldsymbol{\mathrm{India}}\right). \\ $$ Terms of Service Privacy…
Question Number 114933 by mathmax by abdo last updated on 22/Sep/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{\mathrm{cos}\left(\mathrm{2x}\right)}{\mathrm{x}^{\mathrm{4}} \:+\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}}\mathrm{dx} \\ $$ Answered by mathdave last updated on 22/Sep/20…