Question Number 135368 by Bird last updated on 12/Mar/21 $${calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{xarctan}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 12/Mar/21 $${I}\left({a}\right)=\int_{\mathrm{0}}…
Question Number 4298 by Yozzii last updated on 08/Jan/16 $${Find}\:{Q}=\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{3}} }{{e}^{{x}/{T}} −\mathrm{1}}{dx}\:,{where}\:{Q}\:{is} \\ $$$${assumed}\:{finite}\:{for}\:{T}\:{being}\:{a}\: \\ $$$${positive}\:{constant},\:{and}\:{Q}\:{taking}\:{the} \\ $$$${form}\:{Q}={KT}^{{n}} \:,{where}\:{K}={constant} \\ $$$${and}\:{n}\in\mathbb{Z}. \\ $$$$…
Question Number 135371 by Bird last updated on 12/Mar/21 $${let}\:{f}\left({x}\right)={tan}\left(\mathrm{2}{x}\right) \\ $$$${ddvelopp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 4297 by 123456 last updated on 07/Jan/16 $$\mathrm{lets} \\ $$$${f}:\left[\mathrm{0},+\infty\right)\rightarrow\mathbb{R},\forall{x}\geqslant{y}\Rightarrow{f}\left({x}\right)\geqslant{f}\left({y}\right) \\ $$$${g}:\left[\mathrm{0},+\infty\right)\rightarrow\mathbb{R} \\ $$$$\mathrm{if} \\ $$$$\forall{x}\in\left[\mathrm{0},+\infty\right),{f}\left({x}\right)\leqslant{g}\left({x}\right)\leqslant{f}\left(\mathrm{2}{x}\right) \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}{f}\left({x}\right)=\mathrm{L},\mathrm{L}\:\mathrm{is}\:\mathrm{finite} \\ $$$$\mathrm{does} \\ $$$$\underset{{x}\rightarrow+\infty}…
Question Number 135370 by Bird last updated on 12/Mar/21 $${let}\:{f}\left({x}\right)=\frac{\mathrm{1}}{{cosx}\:+\mathrm{2}{sinx}} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 135364 by liberty last updated on 12/Mar/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 135366 by Dwaipayan Shikari last updated on 12/Mar/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt[{\mathrm{6}}]{\mathrm{6}{x}−\mathrm{15}{x}^{\mathrm{2}} +\mathrm{20}{x}^{\mathrm{3}} −\mathrm{15}{x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{5}} −{x}^{\mathrm{6}} }}{dx}=\frac{\pi}{\mathrm{3}} \\ $$$${Or} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt[{{k}}]{{kx}−\frac{{k}\left({k}−\mathrm{1}\right)}{\mathrm{2}}{x}^{\mathrm{2}} +\frac{{k}\left({k}−\mathrm{1}\right)\left({k}−\mathrm{2}\right)}{\mathrm{6}}{x}^{\mathrm{3}}…
Question Number 69829 by TawaTawa last updated on 28/Sep/19 Commented by TawaTawa last updated on 28/Sep/19 $$\mathrm{The}\:\mathrm{question}\:\mathrm{says}\:\mathrm{do}\:\mathrm{not}\:\mathrm{use}\:\mathrm{Newton}'\mathrm{s}\:\mathrm{law}\:\mathrm{and}\:\mathrm{kinematic} \\ $$ Commented by TawaTawa last updated on…
Question Number 135361 by leena12345 last updated on 12/Mar/21 $${f}\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} +\mathrm{6}{x},\left[−\mathrm{1},\mathrm{5}\right] \\ $$$${find}−{the}−{average}−{value} \\ $$$$ \\ $$ Answered by mr W last updated on 12/Mar/21…
Question Number 69827 by Learner-123 last updated on 28/Sep/19 $${The}\:{acceleration}\:{of}\:{a}\:{particle}\:{moving} \\ $$$${in}\:{a}\:{straight}\:{line}\:{is}\:{defined}\:{as}\:{a}=\mathrm{6}{t}−\mathrm{20} \\ $$$${m}/{s}^{\mathrm{2}} ,\:{where}\:{t}\:{is}\:{in}\:{seconds}.\:{Knowing} \\ $$$${that}\:{s}=\mathrm{0}{m}\:{when}\:{t}=\mathrm{3}{s}\:{and}\:{that}\:{t}=\mathrm{5}{sec} \\ $$$${when}\:{v}=\mathrm{2}{m}/{s}.\:{Determine}\:{the}\:{total} \\ $$$${distance}\:{travelled}\:{when}\:{t}=\mathrm{11}{s}. \\ $$ Answered by…