Question Number 138422 by mnjuly1970 last updated on 13/Apr/21 $$\:\:\:\:\:\:\:\:\:…….{nice}\:\:\:\:\:{calculus}….. \\ $$$$\:\:\:{evaluate}: \\ $$$$\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \:\frac{\sqrt[{\mathrm{3}}]{\mathrm{1}+{x}}\:−\sqrt[{\mathrm{3}}]{{x}}}{\:\sqrt{{x}}}\:^{\:\:} {dx}=? \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 138415 by tugu last updated on 13/Apr/21 $${A},{B}\:\in{R},\:\:{f}\left(\mathrm{1}\right)=\mathrm{0}\:,\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left({f}\left({x}\right)\right)^{\mathrm{2}} {dx}\:={A}\:{and}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{xf}\left({x}\right){dx}={B}\: \\ $$$${what}\:{is}\:{the}\:{integral}\:{value}\:{of}\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{xf}\left({x}\right)\left({f}\:'\left({x}\right)−\mathrm{1}\right){dx}\:{by}\:{using}\:{trrms}\:{of}\:{A}\:{and}\:{B}\:?\: \\ $$ Answered by Ar Brandon…
Question Number 138407 by tugu last updated on 13/Apr/21 $${if}\:{the}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{x}}\underset{\mathrm{1}} {\overset{{x}} {\int}}\left(\mathrm{2}{t}−{F}\:'\left({t}\right)\right){dt}\:\:\Rightarrow\:{what}\:{the}\:{F}\:'\left(\mathrm{1}\right)\:{value}\:{using}\:{the}\:{Leibnitz}\:{formula}. \\ $$ Answered by ajfour last updated on 13/Apr/21 $${F}\:'\left({x}\right)=−\frac{{F}\left({x}\right)}{{x}}+\frac{\mathrm{1}}{{x}}\left[\mathrm{2}{x}−{F}\:'\left({x}\right)\right] \\ $$$$\left({x}+\mathrm{1}\right){F}\:'\left({x}\right)+{F}\left({x}\right)=\mathrm{2}{x} \\…
Question Number 138403 by tugu last updated on 13/Apr/21 $$\int\frac{{e}^{\mathrm{4}{t}} }{{e}^{\mathrm{2}{t}} +\mathrm{3}{e}^{{t}} +\mathrm{2}}{dt}=? \\ $$ Answered by bemath last updated on 13/Apr/21 $${let}\:{e}^{{t}} \:=\:{u}\:,\:{e}^{\mathrm{2}{t}} +\mathrm{3}{e}^{{t}}…
Question Number 7300 by Tawakalitu. last updated on 22/Aug/16 $$\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} \:\:\:\frac{{sinx}}{{sinx}\:+\:{cosx}}\:{dx}\: \\ $$ Answered by Yozzia last updated on 22/Aug/16 $${I}=\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{{sinx}}{{sinx}+{cosx}}{dx} \\…
Question Number 72813 by Learner-123 last updated on 03/Nov/19 $${Find}\:{the}\:{area}\:{of}\:{the}\:{region}\:{enclosed} \\ $$$${by}\:{the}\:{line}\:\mathrm{5}{y}={x}+\mathrm{6}\:{and}\:{the}\:{curve} \\ $$$${y}=\sqrt{\mid{x}\mid}\:. \\ $$ Commented by ajfour last updated on 03/Nov/19 Commented by…
Question Number 72796 by Learner-123 last updated on 03/Nov/19 $${Integrate}\:{f}\left({x},{y}\right)=\frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{over} \\ $$$${the}\:{triangle}\:{with}\:{vertices}\:\left(\mathrm{0},\mathrm{0}\right)\:,\left(\mathrm{1},\mathrm{0}\right), \\ $$$$\left(\mathrm{1},\sqrt{\mathrm{3}}\right)\:{after}\:{changing}\:{it}\:{to}\:{polar}\:{form}. \\ $$ Answered by mind is power last…
Question Number 72789 by Learner-123 last updated on 02/Nov/19 $${Find}\:{the}\:{area}\:{of}\:{the}\:{surface}\:{generated} \\ $$$${by}\:{revolving}\:{the}\:{curve}\:{x}=\frac{{y}^{\mathrm{4}} }{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{8}{y}^{\mathrm{2}} }\: \\ $$$${about}\:{the}\:{x}−{axis}\:.\:\left({given}:\mathrm{1}\leqslant{y}\leqslant\mathrm{2}\right) \\ $$ Commented by MJS last updated on 02/Nov/19…
Question Number 138296 by bobhans last updated on 12/Apr/21 $$\int\:\frac{{dx}}{{x}^{\mathrm{4}} \sqrt{{x}^{\mathrm{2}} −{a}^{\mathrm{2}} }}\:=? \\ $$ Answered by bemath last updated on 12/Apr/21 Answered by mathmax…
Question Number 138283 by mnjuly1970 last updated on 11/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:……{advanced}\:\:\:………..\:\:{calculus}…… \\ $$$$\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right).{arctan}\left({x}\right)}{{x}^{\mathrm{2}} }{dx}= \\ $$$$\:{proof}::: \\ $$$$\:\:\:\boldsymbol{\phi}\underset{\langle{substitution}\rangle} {\overset{{x}={tan}\left(\theta\right)} {=}}\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}}…