Question Number 17676 by mondodotto@gmail.com last updated on 09/Jul/17 Answered by alex041103 last updated on 09/Jul/17 $$\mathrm{First}: \\ $$$$\frac{\mathrm{5cos}^{\mathrm{3}} \mathrm{x}\:+\:\mathrm{2sin}^{\mathrm{3}} \mathrm{x}}{\mathrm{2sin}^{\mathrm{2}} \mathrm{xcos}^{\mathrm{2}} \mathrm{x}}\:=\:\frac{\mathrm{5}}{\mathrm{2}}\:\frac{\mathrm{cosx}}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}+\frac{\mathrm{sinx}}{\mathrm{cos}^{\mathrm{2}} \mathrm{x}}…
Question Number 83206 by mathmax by abdo last updated on 28/Feb/20 $$\left.\mathrm{1}\right)\:{find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{{dx}}{\mathrm{2}+{a}\:{sinx}}\:\:\:\:\left({areal}\right) \\ $$$$\left.\mathrm{2}\right)\:{c}\:{explicite}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{{sinx}}{\left(\mathrm{2}+{asinx}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by…
Question Number 83204 by M±th+et£s last updated on 28/Feb/20 $$\int_{{t}−\mathrm{1}} ^{{t}} {ln}\left({x}!\right){dx}=? \\ $$ Commented by MJS last updated on 28/Feb/20 $$\mathrm{if}\:\mathrm{you}\:\mathrm{use}\:{x}!\:\mathrm{it}'\mathrm{s}\:\mathrm{only}\:\mathrm{defined}\:\mathrm{for}\:{x}\in\mathbb{N}\:\Rightarrow\:\mathrm{no} \\ $$$$\mathrm{integral}\:\mathrm{possible} \\…
Question Number 148720 by qaz last updated on 30/Jul/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{Talor}\:\mathrm{series}\:\mathrm{of}\:\frac{\mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)}{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{at}\:\mathrm{x}=\mathrm{0}. \\ $$ Answered by mathmax by abdo last updated on 30/Jul/21 $$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)}{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2}} }\:\:\mathrm{we}\:\mathrm{have}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty}…
Question Number 17625 by tawa tawa last updated on 08/Jul/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{fourier}\:\mathrm{series}\:\mathrm{of}\::\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{x},\:\:\mathrm{from}\:\:\:\mathrm{0}\:<\:\mathrm{x}\:<\:\pi \\ $$ Commented by tawa tawa last updated on 08/Jul/17 $$\mathrm{please}\:\mathrm{help}\:\mathrm{with}\:\mathrm{this}. \\ $$ Answered…
Question Number 83164 by niroj last updated on 28/Feb/20 $$ \\ $$$$ \\ $$$$\:\mathrm{Evaluate}: \\ $$$$\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\:\:\mathrm{1}}{\mathrm{1}+\boldsymbol{\mathrm{cos}}\:\boldsymbol{\alpha}\:\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}} \\ $$ Commented by mathmax by abdo…
Question Number 17604 by tawa tawa last updated on 08/Jul/17 $$\int_{\:\:\mathrm{0}} ^{\:\:\mathrm{n}} \:\mathrm{x}^{\mathrm{2}} \left(\mathrm{n}\:−\:\mathrm{x}\right)^{\mathrm{p}} \:\mathrm{dx}\:\:\:\:\:\:\:\mathrm{for}\:\:\:\mathrm{p}\:>\:\mathrm{0} \\ $$ Answered by sma3l2996 last updated on 08/Jul/17 $${t}={n}−{x}\Rightarrow{dt}=−{dx}…
Question Number 17603 by tawa tawa last updated on 08/Jul/17 $$\int_{\:\:\mathrm{0}} ^{\:\:\mathrm{a}/\mathrm{2}} \:\mathrm{x}^{\mathrm{2}} \left(\mathrm{a}^{\mathrm{2}} \:−\:\mathrm{x}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} \:\mathrm{dx} \\ $$ Answered by alex041103 last updated on…
Question Number 17599 by chux last updated on 08/Jul/17 $$\mathrm{a}\:\mathrm{particle}\:\mathrm{starts}\:\mathrm{with}\:\mathrm{an}\:\mathrm{initial} \\ $$$$\mathrm{speed}\:\mathrm{u},\mathrm{it}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight} \\ $$$$\mathrm{line}\:\mathrm{with}\:\mathrm{an}\:\mathrm{accleration}\:\mathrm{which} \\ $$$$\mathrm{varies}\:\mathrm{as}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of}\:\mathrm{the}\:\mathrm{time} \\ $$$$\mathrm{the}\:\mathrm{particle}\:\mathrm{has}\:\mathrm{been}\:\mathrm{in}\:\mathrm{motion}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{at}\:\mathrm{any}\:\mathrm{time}\:\mathrm{t},\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{distance}\:\mathrm{travelled}. \\ $$ Answered…
Question Number 83123 by M±th+et£s last updated on 28/Feb/20 $$\int\frac{\left({x}^{\mathrm{2}} −\mathrm{1}\right)}{\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right)\left({x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{2}\right)}\:{dx} \\ $$ Commented by mathmax by abdo last updated on 28/Feb/20 $${A}\:=\int\:\:\frac{{x}^{\mathrm{2}}…