Question Number 108920 by mathdave last updated on 20/Aug/20 Answered by 1549442205PVT last updated on 20/Aug/20 $$\mathrm{I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{12}}} \mathrm{ln}\left(\mathrm{tanx}\right)\mathrm{dx}.\mathrm{Put}\:\mathrm{tanx}\:=\mathrm{t} \\ $$$$\Rightarrow\mathrm{dt}=\left(\mathrm{1}+\mathrm{t}^{\mathrm{2}} \right)\mathrm{dx}\Rightarrow\mathrm{I}=\int_{\mathrm{0}} ^{\:\mathrm{2}−\sqrt{\mathrm{3}}} \frac{\mathrm{ln}\left(\mathrm{t}\right)}{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }\mathrm{dt}…
Question Number 174443 by daus last updated on 01/Aug/22 Commented by Rasheed.Sindhi last updated on 01/Aug/22 $${Not}\:{clear}.{Pl}\:{type}. \\ $$ Commented by Rasheed.Sindhi last updated on…
Question Number 108901 by ZiYangLee last updated on 20/Aug/20 $${f}\left({x}\right)={x}^{\mathrm{2}} \left(\mathrm{1}+{x}\right)^{\mathrm{3}} \\ $$$$\mathrm{Find}\:{f}''\left(\mathrm{1}\right).\: \\ $$ Answered by malwaan last updated on 20/Aug/20 $${f}\:'\left({x}\right)={x}^{\mathrm{2}} ×\mathrm{3}\left(\mathrm{1}+{x}\right)^{\mathrm{2}} +\left(\mathrm{1}+{x}\right)^{\mathrm{3}}…
Question Number 108899 by mathdave last updated on 20/Aug/20 Commented by mathdave last updated on 20/Aug/20 $${i}\:{posted}\:{the}\:{solution}\:{of}\:{this}\:\:{problem}\:{then}\:{but}\:{i}\:{later} \\ $$$${discovered}\:{some}\:{err}\:{in}\:{it}\:{but}\:{sha}\:{that}\:{has}\:{been} \\ $$$${averted} \\ $$ Terms of…
Question Number 108897 by mathdave last updated on 20/Aug/20 Commented by mathdave last updated on 20/Aug/20 $${my}\:{earlier}\:{problem}\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 174430 by CElcedricjunior last updated on 31/Jul/22 Answered by som(math1967) last updated on 01/Aug/22 $$\:{I}=\int_{\mathrm{0}} ^{\pi} \frac{{xsinx}}{\mathrm{2}\left(\mathrm{1}+{cos}^{\mathrm{2}} {x}\right)}{dx} \\ $$$$\:=\int_{\mathrm{0}} ^{\pi} \frac{\left(\pi−{x}\right){sin}\left(\pi−{x}\right)}{\mathrm{2}\left\{\mathrm{1}+{cos}^{\mathrm{2}} \left(\pi−{x}\right)\right\}}{dx}…
Question Number 43348 by peter frank last updated on 10/Sep/18 Answered by tanmay.chaudhury50@gmail.com last updated on 10/Sep/18 $$\left.\mathrm{3}\right)\mathrm{2}\left(\frac{{b}}{{a}}+\frac{{b}}{{c}}\right)=\frac{{a}}{{b}}+\frac{{a}}{{c}}+\frac{{c}}{{a}}+\frac{{c}}{{b}} \\ $$$${p}=\frac{{b}}{{a}}\:\:\:\:{q}=\frac{{b}}{{c}}\:\:\:\:\:\frac{{q}}{{p}}=\frac{{a}}{{c}} \\ $$$$\frac{{a}}{{q}}=\frac{{c}}{{p}}={r}\left({say}\right) \\ $$$${a}={rq} \\…
Question Number 174404 by Best1 last updated on 31/Jul/22 Answered by alephzero last updated on 31/Jul/22 $${F}\:'\left(\mathrm{2}\right)\:=\:\left({f}\:\circ\:{g}\right)'\left(\mathrm{2}\right)\:=\:{f}'\left({g}\left(\mathrm{2}\right)\right){g}'\left(\mathrm{2}\right)\:= \\ $$$$=\:{f}'\left(\mathrm{8}\right)×\mathrm{4}\:=\:\mathrm{6}×\mathrm{4}\:=\:\mathrm{24} \\ $$ Terms of Service Privacy…
Question Number 174406 by Best1 last updated on 31/Jul/22 Answered by alephzero last updated on 31/Jul/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{4}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }+\mathrm{2}\right)\:\mathrm{d}{x}\:= \\ $$$$\mathrm{4}\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{2}} \:}\mathrm{d}{x}\:+\int_{\mathrm{0}}…
Question Number 174396 by Best1 last updated on 31/Jul/22 Answered by som(math1967) last updated on 31/Jul/22 $${f}^{!} \left(\boldsymbol{{x}}\right)=\mathrm{2}.\mathrm{3}^{\boldsymbol{{mx}}} .\boldsymbol{{sec}}^{\mathrm{2}} \boldsymbol{{xtanx}}+{m}\mathrm{3}^{{mx}} {ln}\mathrm{3}{sec}^{\mathrm{2}} {x} \\ $$$$\Rightarrow\mathrm{0}+{mln}\mathrm{3}=\mathrm{3}\Rightarrow\boldsymbol{{m}}=\frac{\mathrm{3}}{\boldsymbol{{ln}}\mathrm{3}} \\…