Question Number 43935 by abdo.msup.com last updated on 18/Sep/18 $${find}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}−{cos}^{\mathrm{2}} \left({ax}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{2}\right){calculate}\:{f}^{'} \left({a}\right). \\ $$ Commented by maxmathsup by imad last…
Question Number 43934 by abdo.msup.com last updated on 18/Sep/18 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{+\infty} \:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{4}} \:+{x}^{\mathrm{8}} } \\ $$ Commented by maxmathsup by imad last updated on 19/Sep/18…
Question Number 43923 by pieroo last updated on 17/Sep/18 $$\mathrm{A}\:\mathrm{curve}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},−\mathrm{11}\right)\:\mathrm{and}\:\mathrm{its} \\ $$$$\mathrm{gradient}\:\mathrm{at}\:\mathrm{any}\:\mathrm{point}\:\mathrm{is}\:\boldsymbol{\mathrm{a}}\mathrm{x}^{\mathrm{2}} +\boldsymbol{\mathrm{b}},\:\mathrm{where}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}}\:\mathrm{are} \\ $$$$\mathrm{constants}.\:\mathrm{The}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point} \\ $$$$\left(\mathrm{2},−\mathrm{16}\right)\:\mathrm{is}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\boldsymbol{\mathrm{x}}-\mathrm{axis}.\:\mathrm{Find} \\ $$$$\mathrm{i}.\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}} \\ $$$$\mathrm{ii}.\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{curve} \\ $$ Answered by…
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Question Number 109457 by shahria14 last updated on 23/Aug/20 Answered by Dwaipayan Shikari last updated on 23/Aug/20 $$\int{sin}^{\mathrm{3}} {x}\left(\mathrm{1}−{cos}^{\mathrm{2}} {x}\right){dx} \\ $$$$\int{sin}^{\mathrm{3}} {x}−\int{sin}^{\mathrm{3}} {xcos}^{\mathrm{2}} {x}…
Question Number 43918 by maxmathsup by imad last updated on 17/Sep/18 $$\left.\mathrm{1}\right)\:{find}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{{x}} {ln}\left({t}\right){ln}\left(\mathrm{1}−{t}\right){dt}\:\:\:{with}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({t}\right){ln}\left(\mathrm{1}−{t}\right){dt}\:. \\ $$ Commented by maxmathsup by imad…
Question Number 43914 by maxmathsup by imad last updated on 17/Sep/18 $${find}\:\int\:\:\:\:\frac{{x}}{\:\sqrt{\mathrm{1}+{cosx}}}{dx}\:. \\ $$ Commented by maxmathsup by imad last updated on 19/Sep/18 $${let}\:{A}\:=\:\int\:\:\:\:\:\frac{{x}}{\:\sqrt{\mathrm{1}+{cosx}}}{dx}\:{we}\:{have}\:{A}\:=\:\int\:\:\:\frac{{x}}{\:\sqrt{\mathrm{2}{cos}^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right)}}{dx}…
Question Number 43913 by maxmathsup by imad last updated on 17/Sep/18 $${find}\:\int\:\:\:\:\:\frac{{dx}}{\:\sqrt{\mathrm{1}−{cosx}}\:+\sqrt{\mathrm{1}+{cosx}}} \\ $$$$ \\ $$ Commented by maxmathsup by imad last updated on 18/Sep/18…
Question Number 43909 by abdo.msup.com last updated on 17/Sep/18 $${find}\:{f}\left({a},{t}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dx}}{{a}\:+{t}\:{sinx}} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{sinx}}{\left({a}+{tsinx}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{dx}}{\left({a}+{tsinx}\right)^{\mathrm{2}} }\:. \\ $$ Answered…
Question Number 43906 by abdo.msup.com last updated on 17/Sep/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}\left({x}\right)}{{sh}\left(\mathrm{2}{x}\right)}{dx} \\ $$ Commented by maxmathsup by imad last updated on 20/Sep/18 $${let}\:{A}\:=\:\int_{\mathrm{0}} ^{\infty}…