Question Number 138460 by mnjuly1970 last updated on 13/Apr/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 7385 by Tawakalitu. last updated on 25/Aug/16 $$\int{sin}\left(\mathrm{101}{x}\right)\:.\:{sin}^{\mathrm{90}} \left({x}\right)\:{dx} \\ $$ Commented by Yozzia last updated on 26/Aug/16 $${Let}\:{I}\left({n}\right)=\int{e}^{\mathrm{101}{ix}} {sin}^{{n}} {xdx}\:\:\:\left({n}\in\mathbb{Z}^{\geqslant} \:{i}=\sqrt{−\mathrm{1}}\right) \\…
Question Number 138428 by tugu last updated on 13/Apr/21 $${what}\:{the}\:{area}\:{of}\:\:{area}\:{bounded}\:{by}\:{line} \\ $$$${y}=\:\mid{ln}\:{x}\mid\:{and}\:{y}=\:\mathrm{2}\: \\ $$ Answered by Ñï= last updated on 13/Apr/21 $$\mid{lnx}\mid=\mathrm{2} \\ $$$$\Rightarrow{x}={e}^{\mathrm{2}} ,{e}^{−\mathrm{2}}…
Question Number 72889 by mathmax by abdo last updated on 04/Nov/19 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right){n}^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 72888 by mathmax by abdo last updated on 04/Nov/19 $${let}\:{f}\left({x}\right)=\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{tant}}{\mathrm{2}+{x}\:{cost}}{dt}\:\:{with}\:{x}\:{real} \\ $$$$\left.\mathrm{1}\right){determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){determine}\:{also}\:{g}\left({x}\right)=\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{tant}}{\left(\mathrm{2}+{xcost}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{tant}}{\left(\mathrm{2}+\mathrm{3}{cost}\right)}{dt}\:{and}\:\int_{\frac{\pi}{\mathrm{6}}}…
Question Number 138424 by tugu last updated on 13/Apr/21 $$\mid\underset{\mathrm{1}} {\overset{\sqrt{\mathrm{3}}} {\int}}\:\frac{{e}^{−{x}} {sin}\:{x}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx}\mid\leqslant\frac{\pi}{\mathrm{12}{e}} \\ $$ Commented by mitica last updated on 14/Apr/21 $$\exists{c}\in\left[\mathrm{1},\sqrt{\mathrm{3}}\right],\underset{\mathrm{1}} {\overset{\sqrt{\mathrm{3}}}…
Question Number 138422 by mnjuly1970 last updated on 13/Apr/21 $$\:\:\:\:\:\:\:\:\:…….{nice}\:\:\:\:\:{calculus}….. \\ $$$$\:\:\:{evaluate}: \\ $$$$\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \:\frac{\sqrt[{\mathrm{3}}]{\mathrm{1}+{x}}\:−\sqrt[{\mathrm{3}}]{{x}}}{\:\sqrt{{x}}}\:^{\:\:} {dx}=? \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 138415 by tugu last updated on 13/Apr/21 $${A},{B}\:\in{R},\:\:{f}\left(\mathrm{1}\right)=\mathrm{0}\:,\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left({f}\left({x}\right)\right)^{\mathrm{2}} {dx}\:={A}\:{and}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{xf}\left({x}\right){dx}={B}\: \\ $$$${what}\:{is}\:{the}\:{integral}\:{value}\:{of}\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{xf}\left({x}\right)\left({f}\:'\left({x}\right)−\mathrm{1}\right){dx}\:{by}\:{using}\:{trrms}\:{of}\:{A}\:{and}\:{B}\:?\: \\ $$ Answered by Ar Brandon…
Question Number 138407 by tugu last updated on 13/Apr/21 $${if}\:{the}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{x}}\underset{\mathrm{1}} {\overset{{x}} {\int}}\left(\mathrm{2}{t}−{F}\:'\left({t}\right)\right){dt}\:\:\Rightarrow\:{what}\:{the}\:{F}\:'\left(\mathrm{1}\right)\:{value}\:{using}\:{the}\:{Leibnitz}\:{formula}. \\ $$ Answered by ajfour last updated on 13/Apr/21 $${F}\:'\left({x}\right)=−\frac{{F}\left({x}\right)}{{x}}+\frac{\mathrm{1}}{{x}}\left[\mathrm{2}{x}−{F}\:'\left({x}\right)\right] \\ $$$$\left({x}+\mathrm{1}\right){F}\:'\left({x}\right)+{F}\left({x}\right)=\mathrm{2}{x} \\…
Question Number 138403 by tugu last updated on 13/Apr/21 $$\int\frac{{e}^{\mathrm{4}{t}} }{{e}^{\mathrm{2}{t}} +\mathrm{3}{e}^{{t}} +\mathrm{2}}{dt}=? \\ $$ Answered by bemath last updated on 13/Apr/21 $${let}\:{e}^{{t}} \:=\:{u}\:,\:{e}^{\mathrm{2}{t}} +\mathrm{3}{e}^{{t}}…