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Category: Integration

Question-45334

Question Number 45334 by Meritguide1234 last updated on 12/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 12/Oct/18 $${using}\:{gamma}\:{beta}\:{function} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {t}^{{m}−\mathrm{1}} \left(\mathrm{1}−{t}\right)^{{n}−\mathrm{1}} {dt}=\beta\left({m},{n}\right)=\frac{\lceil\left({m}\right)\lceil\left({n}\right)}{\lceil\left({m}+{n}\right)} \\ $$$$\lceil\left({n}+\mathrm{1}\right)={n}!…

lim-n-1-r-1-n-1-3-r-r-k-1-r-2k-1-

Question Number 110772 by Dwaipayan Shikari last updated on 30/Aug/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{3}^{{r}} {r}!}\underset{{k}=\mathrm{1}} {\overset{{r}} {\prod}}\left(\mathrm{2}{k}−\mathrm{1}\right)\right) \\ $$ Terms of Service Privacy Policy Contact:…

let-a-lt-1-and-f-a-0-1-ln-x-ln-1-ax-dx-1-find-a-explicit-form-of-f-a-2-calculate-g-a-0-1-xln-x-1-ax-dx-3-calculate-0-1-ln-x-ln-2-x-dx-4-calculate-0-1-xln-x-2-x-

Question Number 45235 by maxmathsup by imad last updated on 10/Oct/18 $${let}\:\mid{a}\mid<\mathrm{1}\:{and}\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{1}+{ax}\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xln}\left({x}\right)}{\mathrm{1}+{ax}}{dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{2}+{x}\right){dx} \\…

find-x-1-3-x-dx-

Question Number 45231 by maxmathsup by imad last updated on 10/Oct/18 $${find}\:\int\:\sqrt{\left({x}−\mathrm{1}\right)\left(\mathrm{3}−{x}\right)}{dx} \\ $$ Commented by maxmathsup by imad last updated on 12/Oct/18 $${let}\:{A}\:=\int\:\sqrt{\left({x}−\mathrm{1}\right)\left(\mathrm{3}−{x}\right)}{dx}\:\Rightarrow{A}\:=\int\sqrt{\mathrm{3}{x}−{x}^{\mathrm{2}} −\mathrm{3}+{x}}{dx}=\int\sqrt{−{x}^{\mathrm{2}}…

log-cosx-cos2x-1-cos-2-x-dx-

Question Number 176289 by infinityaction last updated on 15/Sep/22 $$\:\:\int\:\:\frac{\mathrm{log}\:\left(\mathrm{cos}{x}\:+\:\sqrt{\mathrm{cos2}{x}}\right)\:}{\mathrm{1}−\mathrm{cos}^{\mathrm{2}} {x}\:}{dx} \\ $$ Commented by infinityaction last updated on 16/Sep/22 $$\int\boldsymbol{\mathrm{cosec}}^{\mathrm{2}} \boldsymbol{{x}}\:\boldsymbol{\mathrm{log}}\left[\boldsymbol{\mathrm{sin}{x}}\left(\boldsymbol{\mathrm{cotx}}\:+\:\sqrt{\boldsymbol{\mathrm{cot}}^{\mathrm{2}} \boldsymbol{{x}}−\mathrm{1}\:}\right)\boldsymbol{\mathrm{dx}}\right. \\ $$$$\underset{\Psi_{\mathrm{1}}…