Question Number 62179 by Tawa1 last updated on 16/Jun/19 $$\int_{\:\:\mathrm{0}} ^{\:\mathrm{2}\:\sqrt{\mathrm{ln}\:\mathrm{3}}} \:\int_{\:\:\frac{\mathrm{y}}{\mathrm{2}}} ^{\:\sqrt{\mathrm{ln}\:\mathrm{3}}} \:\:\:\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \:\:\mathrm{dx}\:\mathrm{dy} \\ $$ Commented by maxmathsup by imad last updated…
Question Number 127704 by NATTAPONG4359 last updated on 01/Jan/21 $$ \\ $$$${if}\:{f}\left({x}\right)=\begin{cases}{{x}−{n}\:;\:\mathrm{2}{n}\:\leqslant\:{x}\:\leqslant\mathrm{2}{n}+\mathrm{1}}\\{{n}+\mathrm{1}\:;\:\mathrm{2}{n}+\mathrm{1}\leqslant{x}\leqslant\mathrm{2}{n}+\mathrm{2}\:}\end{cases}\:{where}\:\:{n}\:=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},..,\mathrm{9} \\ $$$${find}\:\int_{\mathrm{0}} ^{\mathrm{20}} {f}\left({x}\right){dx} \\ $$ Answered by mahdipoor last updated on 01/Jan/21…
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Question Number 62146 by maxmathsup by imad last updated on 16/Jun/19 $${calculate}\:\int\:\sqrt{\frac{{x}−\mathrm{1}}{{x}^{\mathrm{2}} \:+\mathrm{3}}}{dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 127679 by 676597498 last updated on 31/Dec/20 $${its}\:\mathrm{9}:\mathrm{30}{pm}\:{in}\:{Cameroon} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62145 by maxmathsup by imad last updated on 16/Jun/19 $${calculate}\:\:\int_{\mathrm{0}} ^{\pi} {ln}\left({x}^{\mathrm{2}} −\mathrm{2}{xsin}\theta\:+\mathrm{1}\right){d}\theta \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 62141 by maxmathsup by imad last updated on 15/Jun/19 $${let}\:{A}\:=\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:−{i}\right)^{\mathrm{2}} }\:\:\:\:\:\left(\:{i}^{\mathrm{2}} =−\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A} \\ $$$$\left.\mathrm{2}\right)\:{let}\:{R}\:={Re}\left({A}\right)\:{and}\:{I}\:={Im}\left({A}\right) \\ $$$${find}\:\:{the}\:{value}\:{of}\:{R}\:{and}\:{I}\:. \\ $$…
Question Number 62128 by maxmathsup by imad last updated on 15/Jun/19 $${let}\:{U}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({nx}\right)}{\left({x}^{\mathrm{2}} \:+{n}^{\mathrm{2}} \right)^{\mathrm{3}} }{dx}\:\:{with}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{intrems}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} {n}\:{U}_{{n}} \\…
Question Number 62122 by aliesam last updated on 15/Jun/19 $$\int{e}^{{cos}\left({x}\right)} {sin}\left({sin}\left({x}\right)\right)\:{dx}\: \\ $$ Commented by MJS last updated on 15/Jun/19 $$\int\mathrm{e}^{\mathrm{cos}\:{x}} \mathrm{sin}\:\mathrm{sin}\:{x}\:{dx}=−\frac{\mathrm{i}}{\mathrm{2}}\int\left(\mathrm{e}^{\frac{\mathrm{e}^{\mathrm{i}{x}} −\mathrm{e}^{−\mathrm{i}{x}} }{\mathrm{2}}} −\mathrm{e}^{−\frac{\mathrm{e}^{\mathrm{i}{x}}…
Question Number 127631 by snipers237 last updated on 31/Dec/20 $${Let}\:{f}\in{C}^{\infty} \left(\mathbb{R},\mathbb{R}\right)\:,\:\forall\:{n}\in\mathbb{N}\:\:\:{M}_{{n}} =\mid\mid{f}^{\left({n}\right)} \mid\mid_{\infty} \:\: \\ $$$${and}\:\:{u}_{{n}} =\frac{\mathrm{2}^{{n}−\mathrm{1}} {M}_{{n}} }{{M}_{{n}−\mathrm{1}} }\:\:\:{for}\:{n}\geqslant\mathrm{1}\: \\ $$$${Show}\:{that}\:{if}\:\:\:{M}_{\mathrm{1}} <\sqrt{\mathrm{2}{M}_{\mathrm{0}} {M}_{\mathrm{2}} }\:{then}\:{u}_{{n}}…