Question Number 19666 by Joel577 last updated on 14/Aug/17 $$\int\:{x}^{\mathrm{4}} \sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{1}}\:{dx} \\ $$ Answered by ajfour last updated on 14/Aug/17 $$\:\mathrm{I}=\frac{\mathrm{1}}{\mathrm{2}}\int\mathrm{x}^{\mathrm{3}} \left(\mathrm{2x}\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\right)\mathrm{dx} \\…
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Question Number 150738 by nadovic last updated on 15/Aug/21 $$\mathrm{A}\:\mathrm{point}\:\mathrm{P}\left({x},\:{y}\right)\:\mathrm{moves}\:\mathrm{such}\:\mathrm{that}\:\mathrm{its} \\ $$$$\mathrm{perpendicular}\:\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{line} \\ $$$$\mathrm{12}{x}\:+\:\mathrm{5}{y}\:−\:\mathrm{1}\:=\:\:\mathrm{0}\:\mathrm{is}\:\mathrm{always}\:\mathrm{3}\:{units}.\: \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{that}\:\mathrm{describes}\:\mathrm{the}\: \\ $$$$\mathrm{locus}\:\mathrm{precisely}. \\ $$ Commented by nadovic last updated…
Question Number 85198 by otchereabdullai@gmail.com last updated on 19/Mar/20 $$\mathrm{Find}\:\mathrm{x}\:\mathrm{if}\:\:\:\:^{\mathrm{3}} \sqrt{\mathrm{x}\:}+\sqrt{\mathrm{x}}=\sqrt{\mathrm{12}} \\ $$ Answered by MJS last updated on 19/Mar/20 $$\mathrm{let}\:{x}={y}^{\mathrm{6}} \\ $$$${y}^{\mathrm{3}} +{y}^{\mathrm{2}} −\sqrt{\mathrm{12}}=\mathrm{0}…
Question Number 19659 by thukada last updated on 14/Aug/17 $$\frac{\mathrm{1}+{sec}\theta}{{sec}\theta}=\frac{{sin}^{\mathrm{2}\:} \theta}{\mathrm{1}−{cos}\theta} \\ $$$$ \\ $$ Answered by prakash jain last updated on 14/Aug/17 $$\frac{\mathrm{1}+\mathrm{sec}\:\theta}{\mathrm{sec}\:\theta}=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{sec}\:\theta} \\…
Question Number 150728 by ali1245 last updated on 14/Aug/21 Answered by tabata last updated on 15/Aug/21 $$\mathrm{2}{I}=_{{z}={x}\:} {Re}\:\left(\int_{−\infty} ^{\:\infty} \:\frac{{z}^{\:{a}−\mathrm{1}} }{\left({z}^{\mathrm{2}} +{c}\right)\left({z}^{\mathrm{2}} +{b}\right)}{dz}\right) \\ $$$$…
Question Number 85195 by M±th+et£s last updated on 19/Mar/20 $$\left.\mathrm{1}\right){find}\:{the}\:{area}\:{between} \\ $$$${y}^{\mathrm{2}} =\mathrm{3}{x}\:{and}\:{y}={x}^{\mathrm{2}} −\mathrm{2}{x} \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{sin}^{\mathrm{2}} \left(\theta\right)\:{cos}^{\mathrm{2}} \left(\theta\right)}{\left({cos}^{\mathrm{3}} \left(\theta\right)+{sin}^{\mathrm{3}} \left(\theta\right)\right)^{\mathrm{2}} }\:{d}\theta…
Question Number 19658 by icyfalcon999 last updated on 14/Aug/17 $$=\frac{\mathrm{sec}\:\mathrm{x}−\mathrm{1}}{\mathrm{sec}\:\mathrm{x}+\mathrm{1}} \\ $$$$=\frac{\mathrm{sec}\:\mathrm{x}+\left(\mathrm{1}−\mathrm{1}\right)−\mathrm{1}}{\mathrm{sec}\:\mathrm{x}+\mathrm{1}} \\ $$$$=\frac{\left(\mathrm{sec}\:\mathrm{x}+\mathrm{1}\right)−\mathrm{2}}{\mathrm{sec}\:\mathrm{x}+\mathrm{1}} \\ $$$$=\frac{\mathrm{sec}\:\mathrm{x}+\mathrm{1}}{\mathrm{sec}\:\mathrm{x}+\mathrm{1}}−\frac{\mathrm{2}}{\mathrm{sec}\:\mathrm{x}+\mathrm{1}} \\ $$$$=\mathrm{1}−\frac{\mathrm{2}}{\mathrm{sec}\:\mathrm{x}+\mathrm{1}} \\ $$$$=\mathrm{1}−\mathrm{2}\left(\mathrm{sec}\:\mathrm{x}+\mathrm{1}\right)^{−\mathrm{1}} \\ $$$$\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{1}−\mathrm{2}\left(\mathrm{sec}\:\mathrm{x}+\mathrm{1}\right)^{−\mathrm{1}} \right) \\ $$$$=−\mathrm{2}\left(−\mathrm{1}\left(\mathrm{sec}\:\mathrm{x}+\mathrm{1}\right)^{−\mathrm{2}}…
Question Number 19657 by vivek last updated on 14/Aug/17 $${differentiate}\:{the}\:{function}\:{with}\:{respect}\: \\ $$$${to}\:{x} \\ $$$$\mathrm{1}.\:\:\:\:\frac{{secx}−\mathrm{1}}{{secx}+\mathrm{1}} \\ $$ Commented by prakash jain last updated on 14/Aug/17 $${answer}\:{in}\:{Q}\mathrm{19658}…
Question Number 85191 by sahnaz last updated on 19/Mar/20 $$\int\frac{\mathrm{z}+\mathrm{2}}{\mathrm{z}} \\ $$ Answered by sahnaz last updated on 19/Mar/20 $$\mathrm{dz} \\ $$ Answered by MJS…