Question Number 107212 by bemath last updated on 09/Aug/20 $$\:\:\:\circledcirc{bemath}\circledcirc \\ $$$$\int\:{x}^{\mathrm{6}} \:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:{dx}\:? \\ $$ Answered by Ar Brandon last updated on 09/Aug/20 $$\mathcal{I}=\int\mathrm{x}^{\mathrm{6}}…
Question Number 41678 by math khazana by abdo last updated on 11/Aug/18 $${prove}\:{that}\:\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{\mathrm{2}} \right){dx}=\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{\mathrm{2}} \right){dx}\:{by}\:{using} \\ $$$${only}\:{series}. \\ $$ Answered by…
Question Number 41675 by Raj Singh last updated on 11/Aug/18 Commented by math khazana by abdo last updated on 12/Aug/18 $${I}\:=\:\int\:\:\:\:\frac{{dx}}{\mathrm{1}+\frac{{cosx}}{{sinx}}}\:=\:\int\:\:\:\frac{{sinx}}{{sinx}\:+{cosx}}\:{dx} \\ $$$$=_{{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}} \:\:\:\int\:\:\:\:\frac{\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }}{\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 41677 by math khazana by abdo last updated on 11/Aug/18 $${calculate}\:{A}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{cos}^{\mathrm{8}} {xdx}\:{and}\: \\ $$$${B}=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{sin}^{\mathrm{8}} {xdx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{A}\:+{B}\:{and}\:{A}−{B} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{A}^{\mathrm{2}}…
Question Number 172741 by Kalebwizeman last updated on 30/Jun/22 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}{Sin}\overset{\mathrm{100}} {\:}{xdx} \\ $$ Answered by aleks041103 last updated on 01/Jul/22 $${I}_{{n}} =\mathrm{2}\int_{\mathrm{0}} ^{\pi/\mathrm{2}}…
Question Number 107197 by john santu last updated on 09/Aug/20 $$\:\:\:\:\:\trianglerighteq\mathrm{JS}\trianglelefteq \\ $$$$\int\overset{\:\pi/\mathrm{6}} {\:}_{\mathrm{0}} \mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{6x}\right)\:\mathrm{cos}\:^{\mathrm{4}} \left(\mathrm{3x}\right)\:\mathrm{dx}\:? \\ $$$$\left[\:\mathrm{by}\:\mathrm{using}\:\mathrm{the}\:\mathcal{G}\mathrm{amma}\:\mathrm{function}\:\right] \\ $$ Terms of Service Privacy…
Question Number 41651 by rahul 19 last updated on 10/Aug/18 $$\int\left(\:\mathrm{1}+\mathrm{2}{x}+\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}^{\mathrm{3}} +………\right)\:{dx}\:,\:\:\: \\ $$$$\left(\mathrm{0}<\mid{x}\mid<\mathrm{1}\right) \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 107193 by bobhans last updated on 09/Aug/20 $$\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\frac{\mathrm{ln}\:\mathrm{x}}{\:\sqrt{\mathrm{4x}−\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:? \\ $$ Answered by hgrocks last updated on 09/Aug/20 Commented by bobhans…
Question Number 107184 by bemath last updated on 09/Aug/20 $$\:\:\:\:\:\:\:@{bemath}@ \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\:{x}\:\sqrt[{\mathrm{3}}]{\mathrm{8}−{x}^{\mathrm{3}} }\:{dx}\:=?\: \\ $$ Answered by john santu last updated on 09/Aug/20…
Question Number 172712 by ilhamQ last updated on 30/Jun/22 $$\mathrm{1}.\:\int\frac{{x}}{{x}^{\mathrm{2}} −{x}−\mathrm{6}}\:{dx}=… \\ $$ Answered by Ar Brandon last updated on 30/Jun/22 $$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{x}−\mathrm{1}}{{x}^{\mathrm{2}} −{x}−\mathrm{6}}{dx}+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{1}}{{x}^{\mathrm{2}} −{x}−\mathrm{6}}{dx} \\…