Question Number 78853 by mind is power last updated on 21/Jan/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\left(\mathrm{x}\right)+\mathrm{sin}\left(\mathrm{y}\right)}{\mathrm{x}+\mathrm{y}}\mathrm{dxdy}? \\ $$ Answered by mind is power last updated…
Question Number 78829 by jagoll last updated on 21/Jan/20 $$\mathrm{given}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}+\mathrm{4}\right)\:\forall\mathrm{x}\in\mathbb{R} \\ $$$$\mathrm{and}\:\underset{\mathrm{5}} {\overset{\mathrm{7}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\mathrm{p}\:.\:\mathrm{what}\:\mathrm{is}\: \\ $$$$\underset{\mathrm{2}} {\overset{\mathrm{10}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}? \\ $$$$ \\ $$ Commented by jagoll…
Question Number 144348 by ArielVyny last updated on 24/Jun/21 Commented by Dwaipayan Shikari last updated on 24/Jun/21 $${See}\:{Q}\mathrm{144057} \\ $$ Commented by ArielVyny last updated…
Question Number 78797 by TawaTawa last updated on 20/Jan/20 $$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{e}^{\mathrm{x}} \:−\:\mathrm{1}}\:\mathrm{dx}\:\:\:\:=\:\:\:\frac{\pi^{\mathrm{4}} }{\mathrm{15}} \\ $$ Answered by mind is power last updated on…
Question Number 144323 by qaz last updated on 24/Jun/21 $$\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}+\mathrm{1}} }{\mathrm{n}}=? \\ $$ Answered by mathmax by abdo last updated on 25/Jun/21 $$\mathrm{A}_{\mathrm{n}}…
Question Number 144322 by qaz last updated on 24/Jun/21 $$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2n}\right)!!}{\left(\mathrm{2n}+\mathrm{1}\right)!!\left(\mathrm{n}+\mathrm{1}\right)}\mathrm{x}^{\mathrm{2n}+\mathrm{2}} =?……….\mid\mathrm{x}\mid\leqslant\mathrm{1} \\ $$ Answered by mindispower last updated on 25/Jun/21 $$\left(\mathrm{2}{n}\right)!!=\mathrm{2}^{{n}} .{n}! \\…
Question Number 78766 by M±th+et£s last updated on 20/Jan/20 $$\int\mathrm{2}\:{e}^{\frac{\mathrm{1}}{\mathrm{2}\left({x}−\mathrm{2}\right)^{\mathrm{2}} }} \:{dx} \\ $$ Answered by MJS last updated on 20/Jan/20 $$\mathrm{2}\int\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{2}\left({x}−\mathrm{2}\right)^{\mathrm{2}} }} {dx}= \\…
Question Number 144248 by Pagnol last updated on 23/Jun/21 Answered by Ar Brandon last updated on 23/Jun/21 $$\mathrm{I}=\int\mathrm{tan}^{\mathrm{7}} \mathrm{xdx}=\int\mathrm{tan}^{\mathrm{5}} \mathrm{x}\left(\mathrm{sec}^{\mathrm{2}} \mathrm{x}−\mathrm{1}\right)\mathrm{dx} \\ $$$$\:\:=\frac{\mathrm{tan}^{\mathrm{6}} \mathrm{x}}{\mathrm{6}}−\int\mathrm{tan}^{\mathrm{3}} \mathrm{x}\left(\mathrm{sec}^{\mathrm{2}}…
Question Number 78717 by jagoll last updated on 20/Jan/20 $$\mathrm{given}\: \\ $$$$\int\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}\:\sqrt[{\mathrm{3}\:}]{\mathrm{g}\left(\mathrm{x}\right)}}\:.\: \\ $$$$\mathrm{g}'\left(\mathrm{1}\right)=\:\mathrm{g}\left(\mathrm{1}\right)\:=\:\mathrm{8}\:\Rightarrow\mathrm{f}\left(\mathrm{1}\right)=? \\ $$$$ \\ $$ Commented by john santu last updated on…
Question Number 144245 by ArielVyny last updated on 23/Jun/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{2}{n}} }{\left({x}−\mathrm{1}\right)^{{n}} }{dx} \\ $$ Answered by mathmax by abdo last updated on 23/Jun/21…