Question Number 139217 by mnjuly1970 last updated on 24/Apr/21 $$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:…..\:{nice}\:….\:….\:{math}…. \\ $$$$\:\:\:{prove}\:{that}: \\ $$$$\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{ln}\left(\mathrm{1}+{sin}\left({x}\right).{cos}\left({x}\right)\right)}{{tan}\left({x}\right)}{dx}=\frac{\mathrm{5}\pi^{\mathrm{2}} }{\mathrm{72}} \\ $$ Commented by liki last…
Question Number 8114 by uchechukwu okorie favour last updated on 30/Sep/16 $${Evaluate}\:\int\mathrm{cos}\:^{\mathrm{6}} {x} \\ $$ Answered by sandy_suhendra last updated on 30/Sep/16 Answered by prakash…
Question Number 8115 by uchechukwu okorie favour last updated on 30/Sep/16 $${if}\:{xy}+{y}^{\mathrm{2}} =\mathrm{1}.\:{Find}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}}\:{at}\:\left(\mathrm{0},\mathrm{1}\right) \\ $$ Answered by prakash jain last updated on 30/Sep/16 $${x}\frac{{dy}}{{dx}}+{y}+\mathrm{2}{y}\frac{{dy}}{{dx}}=\mathrm{0}…\left({i}\right)…
Question Number 139182 by aupo14 last updated on 23/Apr/21 Commented by mr W last updated on 23/Apr/21 $${there}\:{is}\:{not}\:{much}\:{to}\:{explain}.\:{it}\:{is} \\ $$$${just}\:{the}\:{definition}\:{of}\:{a}\:{special} \\ $$$${function}. \\ $$ Commented…
Question Number 139164 by mathlove last updated on 23/Apr/21 Answered by qaz last updated on 25/Apr/21 $${ln}\left(\mathrm{1}−{ae}^{{ix}} \right) \\ $$$$={ln}\left[\mathrm{1}−{a}\left(\mathrm{cos}\:{x}+{i}\mathrm{sin}\:{x}\right)\right] \\ $$$$={ln}\left(\sqrt{\left(\mathrm{1}−{a}\mathrm{cos}\:{x}\right)^{\mathrm{2}} +\left({a}\mathrm{sin}\:{x}\right)^{\mathrm{2}} }{e}^{{i}\mathrm{tan}^{−\mathrm{1}} \frac{−{a}\mathrm{sin}\:{x}}{\mathrm{1}−{a}\mathrm{cos}\:{x}}}…
Question Number 139153 by henderson last updated on 23/Apr/21 $$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{everybody}}\:! \\ $$$$\boldsymbol{\mathrm{for}}\:{f}\left({x}\right)=\int_{{x}} ^{\:{x}^{\mathrm{2}} } \:\:\frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{{t}}\:{dt} \\ $$$$\mathrm{1}.\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{domain}}\:\boldsymbol{\mathrm{of}}\:{f},\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:{f}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{even}}. \\ $$$$\mathrm{2}.\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:{f}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{differentiable}}\:\boldsymbol{\mathrm{on}}\:\mathbb{R},\:\boldsymbol{\mathrm{find}}\:{f}\:^{'} \left({x}\right). \\ $$$$\mathrm{3}.\:\boldsymbol{\mathrm{determine}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{expansion}}\:\boldsymbol{\mathrm{limited}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{order}}\:\mathrm{4}\:\boldsymbol{\mathrm{of}}\:{f} \\ $$$$\boldsymbol{\mathrm{in}}\:\mathrm{0}.…
Question Number 8070 by FilupSmith last updated on 29/Sep/16 $$\mathrm{a}\:\mathrm{line}\:{L}\:\mathrm{intersec}{ts}\:\left(\mathrm{0},\:\mathrm{0}\right)\:{and}\:{the}\:{curve} \\ $$$${y}={x}^{\mathrm{2}} \:\:\:{at}\:{x}={t}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}? \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{between}\:{L}\:\mathrm{and}\:{y}\:\mathrm{from} \\ $$$${x}=\mathrm{0}\:\mathrm{to}\:{x}={t}? \\ $$ Answered by sandy_suhendra last…
Question Number 139101 by mnjuly1970 last updated on 22/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…….{nice}\:\:\:{calculus}….. \\ $$$$\boldsymbol{\phi}\overset{???} {=}\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}−{x}}{\mathrm{1}−{xy}}\left(−{ln}\left({xy}\right)\right)^{\mathrm{2019}} {dxdy} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:……… \\ $$ Answered by Dwaipayan…
Question Number 139092 by mathdanisur last updated on 22/Apr/21 $$\Omega=\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{xsinh}\left(\pi{x}\right){e}^{−{x}^{\mathrm{2}} } }{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 8015 by tawakalitu last updated on 28/Sep/16 $$\int\frac{\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{2}} }}{\mathrm{1}\:+\:{x}}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com