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Category: Integration

A-region-is-enclosed-by-curves-x-2-4y-x-2-4y-x-4-amp-x-4-V-1-is-the-volume-of-the-solid-obtained-by-rotating-the-above-region-round-the-y-axis-Another-regions-consists-of-points-x-y-satisf

Question Number 144771 by imjagoll last updated on 29/Jun/21 $$\mathrm{A}\:\mathrm{region}\:\mathrm{is}\:\mathrm{enclosed}\:\mathrm{by}\:\mathrm{curves} \\ $$$$\mathrm{x}^{\mathrm{2}} =\mathrm{4y},\:\mathrm{x}^{\mathrm{2}} =−\mathrm{4y},\:\mathrm{x}=\mathrm{4}\:\&\:\mathrm{x}=−\mathrm{4} \\ $$$$\mathrm{V}_{\mathrm{1}} \mathrm{is}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{solid}\:\mathrm{obtained} \\ $$$$\mathrm{by}\:\mathrm{rotating}\:\mathrm{the}\:\mathrm{above}\:\mathrm{region}\:\mathrm{round} \\ $$$$\mathrm{the}\:\mathrm{y}−\mathrm{axis}.\:\:\mathrm{Another}\:\mathrm{regions} \\ $$$$\mathrm{consists}\:\mathrm{of}\:\mathrm{points}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{satisfying} \\ $$$$\mathrm{x}^{\mathrm{2}}…

Question-144764

Question Number 144764 by nonh1 last updated on 29/Jun/21 Answered by liberty last updated on 29/Jun/21 $$\int_{\mathrm{0}} ^{\:\sqrt{\mathrm{ln}\:\mathrm{2}}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}\mathrm{xe}^{\mathrm{x}^{\mathrm{2}} } \:\left(\frac{\mathrm{d}\left(\mathrm{1}+\mathrm{y}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{y}^{\mathrm{2}} }\right)\mathrm{dx}…

Question-144756

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}…

On-souhaite-calculer-I-0-sint-t-dt-1-On-de-finit-la-fonction-F-x-0-e-tx-sint-t-dt-a-De-terminer-le-domaine-de-de-finition-de-f-sur-R-

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}}…

Nice-Calculus-f-x-tan-x-cot-x-R-f-Hint-x-Max-

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\}\:…