Question Number 175042 by peter frank last updated on 17/Aug/22 Answered by Frix last updated on 18/Aug/22 $$\int\frac{{a}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \:{x}\:+{b}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \:{x}}{{a}^{\mathrm{4}} \mathrm{sin}^{\mathrm{4}} \:{x}\:+{b}^{\mathrm{4}} \mathrm{cos}^{\mathrm{4}}…
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Question Number 43939 by abdo.msup.com last updated on 18/Sep/18 $${find}\:{f}\left(\xi\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\mathrm{1}+\left({t}−{i}\xi\right)^{\mathrm{2}} } \\ $$$${and}\:{calculate}\:{f}^{'} \left(\xi\right) \\ $$ Commented by maxmathsup by imad last updated…
Question Number 43938 by abdo.msup.com last updated on 18/Sep/18 $${calvulste}\:{A}_{{n}} =\int_{\mathrm{0}} ^{{n}} \:{t}^{\mathrm{2}} \left[\frac{\mathrm{1}}{\left({t}+\mathrm{1}\right)^{\mathrm{3}} }\right]{dt} \\ $$$${and}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$ Commented by maxmathsup by imad…
Question Number 43937 by abdo.msup.com last updated on 18/Sep/18 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\mathrm{2}{x}+\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{5}}}{dx} \\ $$ Commented by maxmathsup by imad last updated on 19/Sep/18 $${let}\:{A}\:=\:\int_{\mathrm{0}}…
Question Number 109472 by john santu last updated on 24/Aug/20 Answered by 1549442205PVT last updated on 24/Aug/20 $$\mathrm{Put}\:\mathrm{F}=\int\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }} \\ $$$$\mathrm{Putting}\:\:\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }+\mathrm{1}=\mathrm{u}^{\mathrm{2}} \Rightarrow\mathrm{2udu}=\frac{−\mathrm{2}}{\mathrm{x}^{\mathrm{3}} }\mathrm{dx}…
Question Number 43935 by abdo.msup.com last updated on 18/Sep/18 $${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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