Question Number 135610 by mnjuly1970 last updated on 14/Mar/21 $$\:\:\:\:\:\:\:\:\:\:….\:\mathscr{A}{dvanced}\:\:……\:\:\mathscr{C}{alculus}…. \\ $$$$\:\:\:\:\:\:\:\:\:{prove}\:{that}\:: \\ $$$$\:\:\:\begin{array}{|c|c|}{{i}\:::\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\prod}}\left(\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }\right)\:={cos}\left(\frac{\pi{x}}{\mathrm{2}}\right)\:\:\:\:\checkmark\:\:}\\{{ii}\:::\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{{x}^{\mathrm{2}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }\right)=\:{cosh}\left(\frac{\pi{x}}{\mathrm{2}}\right)\:\checkmark\checkmark}\\\hline\end{array}\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…………. \\…
Question Number 4521 by nabilah last updated on 05/Feb/16 $$\int\left(\mathrm{3}{x}+\mathrm{2}\hat {\right)}\mathrm{4} \\ $$ Answered by FilupSmith last updated on 05/Feb/16 $$\mathrm{If}\:\mathrm{you}\:\mathrm{mean}: \\ $$$$\int\left(\mathrm{3}{x}+\mathrm{2}\right)\mathrm{4}{dx} \\ $$$$=\mathrm{4}\int\left(\mathrm{3}{x}+\mathrm{2}\right){dx}…
Question Number 70031 by Nithin Kumar last updated on 30/Sep/19 $$\int\left[{x}\right]{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 135559 by john_santu last updated on 14/Mar/21 Commented by john_santu last updated on 14/Mar/21 $${old}\:{unswered} \\ $$ Answered by bemath last updated on…
Question Number 135525 by mnjuly1970 last updated on 13/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….\:{nice}\:…………….\:{calculus}… \\ $$$$\:\:\:\:\:{evaluation}\:{of}\:::\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} {xe}^{−{x}} \sqrt{\mathrm{1}−{e}^{−{x}} }\:{dx} \\ $$$$\:\:\:\:{solution}::\: \\ $$$$\:\:\:\:\mathrm{1}−{e}^{−{x}} ={t}\:\:\Rightarrow\:\left\{_{\:{x}=−{ln}\left(\mathrm{1}−{t}\right)} ^{\:{e}^{−{x}} {dx}={dt}} \right. \\…
Question Number 135513 by Gaurav500 last updated on 13/Mar/21 Answered by MJS_new last updated on 13/Mar/21 $$\int\frac{{dx}}{\:\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}+\sqrt{{x}+\mathrm{2}}}= \\ $$$$\:\:\:\:\:\left[{t}={x}+\mathrm{1}\:\rightarrow\:{dx}={dt}\right] \\ $$$$=\int\frac{{dt}}{\:\sqrt{{t}−\mathrm{1}}+\sqrt{{t}}+\sqrt{{t}+\mathrm{1}}}=\underset{{k}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}{I}_{{k}} \:+{Ci} \\…
Question Number 135495 by greg_ed last updated on 13/Mar/21 $$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{guyz}}\:! \\ $$$$\boldsymbol{\mathrm{let}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{try}}\:\boldsymbol{\mathrm{this}}\::\:\boldsymbol{\mathrm{I}}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\boldsymbol{{sin}}^{\mathrm{2}} \boldsymbol{{x}}}{\boldsymbol{{cos}}^{\mathrm{3}} \boldsymbol{{x}}}\boldsymbol{{dx}}. \\ $$ Answered by mathmax by abdo last updated…
Question Number 135443 by 0731619177 last updated on 13/Mar/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 4344 by Filup last updated on 12/Jan/16 $$\mathrm{for}\:\int{f}\left({x}\right){dx}={F}\left({x}\right)+{c} \\ $$$$\mathrm{and}\:{sgn}\left({x}\right)=\frac{{x}}{\mid{x}\mid}=\frac{\mid{x}\mid}{{x}}\:\:\:\forall{x}\neq\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{let}\:\mathrm{sgn}\left({x}\right)=\mathrm{0}\:\mathrm{for}\:{x}=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{does}\: \\ $$$$\int{sgn}\left({f}\left({x}\right)\right){f}\left({x}\right){dx}={sgn}\left({f}\left({x}\right)\right)\int{f}\left({x}\right){dx} \\ $$$$\because{sgn}\left({f}\left({x}\right)\right)\:\mathrm{is}\:\mathrm{just}\:\mathrm{a}\:\mathrm{constant}\:\pm\mathrm{1}\:\mathrm{or}\:\mathrm{0}. \\ $$ Commented…
Question Number 135389 by Bird last updated on 12/Mar/21 $${let}\:{U}_{{n}} =\int_{−\infty} ^{\infty} \:\:\frac{{cos}\left({nx}\right)}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$${calculate}\:{lim}_{{n}\rightarrow\infty} {e}^{{n}^{\mathrm{2}} } {U}_{{n}} \\ $$ Terms of Service…