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Category: Integration

Question-109472

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}…

A-curve-passes-through-the-point-1-11-and-its-gradient-at-any-point-is-ax-2-b-where-a-and-b-are-constants-The-tangent-to-the-curve-at-the-point-2-16-is-parallel-to-the-x-axis-Find-i-the-val

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…

1-find-f-x-0-x-ln-t-ln-1-t-dt-with-0-x-1-2-find-the-value-of-0-1-ln-t-ln-1-t-dt-

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…