Question Number 119852 by benjo_mathlover last updated on 27/Oct/20 $$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}^{\mathrm{2}} \:\int\:\underset{\mathrm{0}} {\overset{\frac{\mathrm{1}}{{n}}} {\:}}{x}^{{x}+\mathrm{1}} \:{dx}\:=? \\ $$ Answered by Olaf last updated on 27/Oct/20 $$\int_{\mathrm{0}}…
Question Number 119821 by bemath last updated on 27/Oct/20 $$\:\underset{−\mathrm{3}} {\overset{\mathrm{0}} {\int}}\:\frac{\mathrm{6}{x}−\mathrm{6}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}}}\:{dx}\:=? \\ $$ Answered by bobhans last updated on 27/Oct/20 $$\:\underset{−\mathrm{3}} {\overset{\mathrm{0}} {\int}}\:\frac{\mathrm{6}\left({x}−\mathrm{1}\right)}{\:\sqrt{\left({x}−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 54273 by rahul 19 last updated on 01/Feb/19 Answered by tanmay.chaudhury50@gmail.com last updated on 01/Feb/19 $$\frac{{df}}{{dx}}={f}\left({x}\right)+\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx} \\ $$$$\frac{{df}}{{dx}}={f}\left({x}\right)+{a} \\ $$$$\frac{{df}}{{f}\left({x}\right)+{a}}={dx} \\…
Question Number 54259 by 951172235v last updated on 01/Feb/19 Commented by Meritguide1234 last updated on 01/Feb/19 Answered by rahul 19 last updated on 01/Feb/19 $$\mathrm{1}.…
Question Number 119784 by bemath last updated on 27/Oct/20 $$\:\:\int\:\frac{{dx}}{\:\sqrt{\left(\mathrm{4}{x}−{x}^{\mathrm{2}} \right)^{\mathrm{3}} }} \\ $$$$ \\ $$ Answered by bobhans last updated on 27/Oct/20 $$\int\:\frac{{dx}}{\:\left(\mathrm{4}−\left(\mathrm{2}−{x}\right)^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}}…
Question Number 54248 by rahul 19 last updated on 01/Feb/19 Commented by rahul 19 last updated on 01/Feb/19 $$\left.{Ans}.\:{for}\:\mathrm{3}\right)\rightarrow\:\mathrm{2}\pi^{\mathrm{2}} . \\ $$$$\left.{for}\:\mathrm{2}\right)\rightarrow\:{put}\:{x}=\mathrm{tan}\theta\:{and}\:{then}\:{use} \\ $$$${the}\:{property}\:{of}\:{replacing}\:{x}\:{by}\:{a}+{b}−{x}. \\…
Question Number 54240 by 951172235v last updated on 01/Feb/19 Commented by rahul 19 last updated on 01/Feb/19 $${a}=\mathrm{2}\:,\:{b}=\mathrm{3},{c}=\mathrm{8},{d}=\mathrm{2008}. \\ $$ Answered by rahul 19 last…
Question Number 119773 by bemath last updated on 26/Oct/20 $$\underset{−\mathrm{4}} {\overset{\mathrm{4}} {\int}}\:{x}^{\mathrm{3}} \sqrt{\mathrm{16}−{x}^{\mathrm{2}} \:}\:\mathrm{sec}\:{x}\:{dx}\: \\ $$ Answered by MJS_new last updated on 27/Oct/20 $${f}\left({x}\right)={x}^{\mathrm{3}} \sqrt{\mathrm{16}−{x}^{\mathrm{2}}…
Question Number 119762 by mathmax by abdo last updated on 26/Oct/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{x}^{\mathrm{4}} \mathrm{dx}}{\left(\mathrm{2x}+\mathrm{1}\right)^{\mathrm{5}} \left(\mathrm{3x}+\mathrm{1}\right)^{\mathrm{8}} } \\ $$ Answered by Olaf last updated on…
Question Number 54224 by rahul 19 last updated on 31/Jan/19 $$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{\mathrm{sin}{x}+\mathrm{cos}{x}}{\mathrm{16}+\mathrm{9sin2}{x}}\:{dx}\:=? \\ $$ Commented by Meritguide1234 last updated on 01/Feb/19 $$\Rightarrow\int_{\mathrm{0}} ^{\pi/\mathrm{4}} \frac{\mathrm{sinx}+\mathrm{cosx}}{\mathrm{25}−\mathrm{9}\left(\mathrm{sinx}−\mathrm{cosx}\right)^{\mathrm{2}}…