Question Number 85384 by sakeefhasan05@gmail.com last updated on 21/Mar/20 Commented by mathmax by abdo last updated on 21/Mar/20 $${let}\:{A}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{4}} }\:\Rightarrow\:{A}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}}…
Question Number 150916 by tabata last updated on 16/Aug/21 $${x}^{\left({x}−\mathrm{1}\right)^{\mathrm{2}} } =\mathrm{2}{x}+\mathrm{1}\: \\ $$$$ \\ $$$${how}\:{can}\:{it}\:{solve}\:{this}\:?{help}\:{me}\:{please} \\ $$ Answered by MJS_new last updated on 17/Aug/21…
Question Number 85383 by M±th+et£s last updated on 21/Mar/20 $$\int\sqrt[{\mathrm{5}}]{\frac{{sin}\left({x}\right)}{{cos}^{\mathrm{11}} \left({x}\right)}}\:{dx} \\ $$ Answered by john santu last updated on 21/Mar/20 $$\int\:\:\:\frac{\sqrt[{\mathrm{5}\:}]{\mathrm{tan}\:{x}}}{\mathrm{cos}\:^{\mathrm{2}} {x}}\:{dx}\:=\:\int\:\:\sqrt[{\mathrm{5}\:\:}]{\mathrm{tan}\:{x}}\:{d}\left(\mathrm{tan}\:{x}\right) \\ $$$$=\:\frac{\mathrm{5}}{\mathrm{6}}\:\sqrt[{\mathrm{5}\:\:}]{\left(\mathrm{tan}\:{x}\right)^{\mathrm{6}}…
Question Number 150918 by mathdanisur last updated on 16/Aug/21 Commented by puissant last updated on 16/Aug/21 $$=\:\left[\frac{\underset{{k}=\mathrm{0}} {\overset{\mathrm{1995}} {\sum}}\mathrm{2}^{{k}} }{\mathrm{1997}}\right]\: \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{1997}}\left(\frac{\mathrm{1}−\mathrm{2}^{\mathrm{1996}} }{\mathrm{1}−\mathrm{2}}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{1997}}\left(\mathrm{2}^{\mathrm{1996}}…
Question Number 85374 by M±th+et£s last updated on 21/Mar/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{7}} +{x}^{\mathrm{3}} +\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}\:{dx}\: \\ $$ Commented by MJS last updated on 21/Mar/20 $$\frac{{x}^{\mathrm{7}}…
Question Number 85372 by john santu last updated on 21/Mar/20 $$\mathrm{sin}\:^{\mathrm{2}} {x}−\mathrm{4cos}\:^{\mathrm{2}} {x}\:=\:\mathrm{3}\:\mathrm{sin}\:{x}\:\mathrm{cos}\:{x} \\ $$$${find}\:\mathrm{tan}\:{x}.\: \\ $$ Answered by john santu last updated on 21/Mar/20…
Question Number 150903 by puissant last updated on 16/Aug/21 $${let}\:{x},{y}>\mathrm{0}\:,\:{n}\in\mathbb{N}, \\ $$$${show}\:{that}\:\left({x}+{y}\right)^{{n}} \leqslant\mathrm{2}^{{n}−\mathrm{1}} \left({x}^{{n}} +{y}^{{n}} \right).. \\ $$ Answered by qaz last updated on 16/Aug/21…
Question Number 85364 by Power last updated on 21/Mar/20 Commented by Power last updated on 21/Mar/20 $$ \\ $$ Commented by Power last updated on…
Question Number 85365 by Power last updated on 21/Mar/20 Answered by jagoll last updated on 21/Mar/20 $$\mathrm{C}\:=\:\mathrm{S}_{\mathrm{112}} \:=\:\frac{\mathrm{112}}{\mathrm{2}}\left(−\mathrm{4}+\left(\mathrm{111}×\left(−\mathrm{8}\right)\right)\right. \\ $$$$=\:\mathrm{56}\:×\left(−\mathrm{892}\right) \\ $$$$=\:−\mathrm{49952} \\ $$ Commented…
Question Number 19828 by NECC last updated on 16/Aug/17 $${The}\:{speed}\:{of}\:{a}\:{train}\:{is}\:{reduced} \\ $$$${from}\:\mathrm{80}{km}/{h}\:{to}\:\mathrm{40}{km}/{h}\:{after} \\ $$$${the}\:{application}\:{of}\:{the}\:{brake}. \\ $$$$\left({i}\right){how}\:{much}\:{further}\:{would}\:{the}\: \\ $$$${train}\:{travel}\:{before}\:{coming}\:{to}\:{rest} \\ $$$$\left({ii}\right){assuming}\:{the}\:{acceleration}\:{is} \\ $$$${kept}\:{constant},{how}\:{long}\:{will}\:{it} \\ $$$${take}\:{to}\:{bring}\:{the}\:{train}\:{to}\:{rest} \\…