Question Number 201582 by MathedUp last updated on 09/Dec/23 $$\mathrm{Solve}…. \\ $$$${y}''\left({t}\right)−\mathrm{sin}\left({t}\right){y}\left({t}\right)=\mathrm{0}\:,\: \\ $$$${y}^{\left(\mathrm{2}\right)} \left(\mathrm{0}\right)=\mathrm{0}\:,\:{y}^{\left(\mathrm{1}\right)} \left(\mathrm{0}\right)=−\mathrm{1}\:,\:{y}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\boldsymbol{\mathcal{L}}\left\{{y}''\left({t}\right)−\mathrm{sin}\left({t}\right){y}\left({t}\right)\right\}=\mathrm{0} \\ $$$${s}^{\mathrm{2}} \boldsymbol{\mathrm{F}}\left({s}\right)−{sy}\left(\mathrm{0}\right)−{y}'\left(\mathrm{0}\right)−\boldsymbol{\mathcal{L}}\left\{\mathrm{sin}\left({t}\right){y}\left({t}\right)\right\}=\mathrm{0} \\ $$$$\mathrm{Holy}…×\mathrm{uck}…
Question Number 201573 by sonukgindia last updated on 09/Dec/23 Answered by witcher3 last updated on 09/Dec/23 $$=\int_{−\infty} ^{\infty} \frac{\mathrm{e}^{−\mathrm{2024x}} +\mathrm{e}^{−\mathrm{2020}} }{\left(\mathrm{e}^{−\mathrm{2025x}} +\mathrm{e}^{−\mathrm{2019x}} \right)\left(\left(−\mathrm{4x}^{\mathrm{3}} +\left(\mathrm{4x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}}…
Question Number 201533 by Rodier97 last updated on 08/Dec/23 $$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{Un}\:=\:{ln}\:\left({cos}\:\frac{\mathrm{1}}{\mathrm{2}^{{n}} }\:\right) \\ $$$$\:\:\:\:{show}\:\:{that}\:{Un}\:\leqslant\mathrm{0} \\ $$$$ \\ $$$$ \\ $$$$…
Question Number 201516 by sonukgindia last updated on 08/Dec/23 Answered by Calculusboy last updated on 08/Dec/23 $$\boldsymbol{{Solution}}:\:\boldsymbol{{let}}\:\boldsymbol{{y}}=\frac{\boldsymbol{\pi}}{\mathrm{2}}−\boldsymbol{{x}}\:\:\:\boldsymbol{{dy}}=−\boldsymbol{{dx}} \\ $$$${when}\:\boldsymbol{{x}}=\frac{\boldsymbol{\pi}}{\mathrm{2}}\:\:\:\boldsymbol{{y}}=\mathrm{0}\:\:\boldsymbol{{and}}\:\boldsymbol{{when}}\:\boldsymbol{{x}}=\mathrm{0}\:\:\boldsymbol{{y}}=\frac{\boldsymbol{\pi}}{\mathrm{2}} \\ $$$$\boldsymbol{{I}}=\int_{\frac{\boldsymbol{\pi}}{\mathrm{2}}} ^{\mathrm{0}} \:\frac{\mathrm{1}}{\mathrm{1}+\left[\boldsymbol{{tan}}\left(\frac{\boldsymbol{\pi}}{\mathrm{2}}−\boldsymbol{{y}}\right)\right]^{\boldsymbol{{n}}} }\left(−\boldsymbol{{dy}}\right)\:\:\:\Leftrightarrow\:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}}…
Question Number 201517 by sonukgindia last updated on 08/Dec/23 Answered by Calculusboy last updated on 08/Dec/23 $$\boldsymbol{{Solution}}:\:\boldsymbol{{let}}\:\boldsymbol{\theta}=\frac{\boldsymbol{\pi}}{\mathrm{2}}−\boldsymbol{{x}}\:\:\boldsymbol{{d}\theta}=−\boldsymbol{{dx}} \\ $$$$\boldsymbol{{when}}\:\boldsymbol{{x}}=\frac{\boldsymbol{\pi}}{\mathrm{2}}\:\:\:\boldsymbol{\theta}=\mathrm{0}\:\:\boldsymbol{{and}}\:\boldsymbol{{when}}\:\boldsymbol{{x}}=\mathrm{0}\:\:\boldsymbol{\theta}=\frac{\boldsymbol{\pi}}{\mathrm{2}} \\ $$$$\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \frac{\mathrm{1}}{\mathrm{1}+\left(\frac{\mathrm{1}}{\boldsymbol{{tanx}}}\right)^{\boldsymbol{{n}}} }\boldsymbol{{dx}}\:\:\Leftrightarrow\:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}}…
Question Number 201519 by vahid last updated on 08/Dec/23 Answered by cortano12 last updated on 08/Dec/23 $$\left(\mathrm{1}\right)\:\int\:\frac{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}}{\mathrm{cos}\:^{\mathrm{6}} \mathrm{x}}\:\mathrm{dx}\:=\:−\int\:\frac{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{cos}\:^{\mathrm{6}} \mathrm{x}}\:\mathrm{d}\left(\mathrm{cos}\:\mathrm{x}\right) \\ $$ Answered by…
Question Number 201544 by sonukgindia last updated on 08/Dec/23 Answered by aleks041103 last updated on 09/Dec/23 $${J}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{4}{sin}^{\mathrm{2}} \left({ln}\left({x}\right)\right)}{{ln}\left(\mathrm{1}/{x}\right)}{dx}=−\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{4}{sin}^{\mathrm{2}} \left(\mathrm{1}.{ln}\left({x}\right)\right)}{{ln}\left({x}\right)}{dx} \\ $$$${I}\left({s}\right)=−\int_{\mathrm{0}}…
Question Number 201514 by sonukgindia last updated on 08/Dec/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 201515 by sonukgindia last updated on 08/Dec/23 Answered by Calculusboy last updated on 08/Dec/23 $$\boldsymbol{{Solution}}:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \:\frac{\mathrm{1}}{\mathrm{1}+\left(\frac{\mathrm{1}}{\boldsymbol{{tanx}}}\right)^{\sqrt{\mathrm{2}}} }\boldsymbol{{dx}}\:\:\Leftrightarrow\:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \:\frac{\mathrm{1}}{\frac{\left(\boldsymbol{{tanx}}\right)^{\sqrt{\mathrm{2}}} +\mathrm{1}}{\left(\boldsymbol{{tanx}}\right)^{\sqrt{\mathrm{2}}} }}\boldsymbol{{dx}} \\…
Question Number 201495 by Rodier97 last updated on 07/Dec/23 $$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\left({Un}\right)_{{n}\geqslant\mathrm{1}\:;} \:\:\:\:\frac{\mathrm{1}}{{nC}_{\mathrm{2}{n}} ^{{n}} \:} \\ $$$$ \\ $$$$\:\:\:\:{study}\:\:{convergence}…