Question Number 79222 by mind is power last updated on 23/Jan/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} }{\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}{x}^{{k}} }{dx}=? \\ $$ Commented by mathmax by abdo…
Question Number 144756 by mondlihk last updated on 28/Jun/21 Commented by Mathspace last updated on 28/Jun/21 Answered by Olaf_Thorendsen last updated on 28/Jun/21 $$\Omega\:=\:\int\int_{\mathcal{D}\:=\:\left\{{x}\geqslant\mathrm{0},\:{y}\geqslant\mathrm{0},\:{x}+{y}\leqslant\mathrm{1}\right\}} {xy}\:{dxdy}…
Question Number 144738 by Ar Brandon last updated on 28/Jun/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{On}\:\mathrm{souhaite}\:\mathrm{calculer}\:\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}{t}}{{t}}{dt}. \\ $$$$\left(\mathrm{1}\right)\:\mathrm{On}\:\mathrm{d}\acute {\mathrm{e}finit}\:\mathrm{la}\:\mathrm{fonction}\:{F}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} {e}^{−{tx}} \frac{\mathrm{sin}{t}}{{t}}{dt}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{a}\right)\:\mathrm{D}\acute {\mathrm{e}terminer}\:\mathrm{le}\:\mathrm{domaine}\:\mathrm{de}\:\mathrm{d}\acute {\mathrm{e}finition}\:\mathrm{de}\:{f}\:\mathrm{sur}\:\mathbb{R}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{Montrer}\:\mathrm{que}\:{F}\:\mathrm{est}\:\mathrm{de}\:\mathrm{classe}\:{C}^{\mathrm{1}}…
Question Number 144720 by mnjuly1970 last updated on 28/Jun/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..\mathrm{calculus}….. \\ $$$$\: \\ $$$$\Omega\::=\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sech}\left(\pi{x}\right)}{\mathrm{1}+\mathrm{4}{x}^{\:\mathrm{2}} }\:{dx}\:\overset{?} {=}\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{Ln}\left(\mathrm{2}\right) \\ $$$$ \\ $$$$ \\ $$ Answered…
Question Number 79186 by john santu last updated on 23/Jan/20 $$\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{cos}\:\left({x}\right)}{\mathrm{1}+{e}^{\frac{\mathrm{1}}{{x}}} }\:{dx}\:? \\ $$ Answered by mind is power last updated on 23/Jan/20…
Question Number 144721 by mnjuly1970 last updated on 28/Jun/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:………\:\mathrm{Nice}\:……\ast\ast\ast……\mathrm{Calculus}……… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{f}\:\left(\:\mathrm{x}\:\right)\::\:=\:\left[\:\mathrm{tan}\:\left(\mathrm{x}\right)\:+\:\mathrm{cot}\:\left(\mathrm{x}\right)\:\right] \\ $$$$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{R}_{\:\mathrm{f}\:\:} \:=\:? \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Hint}::\:\:\:\left[\:\mathrm{x}\:\right]\::=\:\mathrm{Max}\:\left\{\:\mathrm{m}\:\in\mathbb{Z}\:\mid\:\mathrm{m}\:\leqslant\:\mathrm{x}\:\right\}\:…
Question Number 79187 by john santu last updated on 23/Jan/20 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{cos}\:\left({nx}\right)−\mathrm{cos}\:\left({n}\alpha\right)}{\mathrm{cos}\:\left({x}\right)−\mathrm{cos}\:\left(\alpha\right)}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 144705 by imjagoll last updated on 28/Jun/21 $$\:\:\int\:\frac{\mathrm{x}^{\mathrm{n}−\mathrm{1}} }{\mathrm{x}^{\mathrm{3n}+\mathrm{1}} \:\left(\mathrm{x}^{\mathrm{n}} −\mathrm{a}\right)}\:\mathrm{dx}\:? \\ $$ Answered by liberty last updated on 28/Jun/21 $$\:\mathrm{let}\:\mathrm{x}^{\mathrm{n}} =\:\mathrm{y} \\…
Question Number 144691 by mnjuly1970 last updated on 27/Jun/21 Answered by mnjuly1970 last updated on 27/Jun/21 $$\:\:\:{ans}: \\ $$$$\:\:\:\:\:{a}\:,{b}\:,\:{c}\:\:\:\:\:\:\:,\:\:{x}\:,\:{y}\:,\:{z}\:\:\:{positive}\:{real} \\ $$$$\:{number}\:: \\ $$$$\:\:{titus}\:{lemma}: \\ $$$$\:\:\frac{{a}^{\mathrm{2}}…
Question Number 13622 by Tinkutara last updated on 21/May/17 $$\mathrm{Evaluate}:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} {e}^{\frac{{x}}{\mathrm{2}}} \mathrm{sin}\:\left(\frac{{x}}{\mathrm{2}}\:+\:\frac{\pi}{\mathrm{4}}\right){dx} \\ $$ Answered by ajfour last updated on 22/May/17 $${I}=\int_{\mathrm{0}} ^{\:\:\mathrm{2}\pi} {e}^{\boldsymbol{{x}}/\mathrm{2}}…