Question Number 103825 by mohammad17 last updated on 17/Jul/20 $$\int\:\frac{{dx}}{\left(\mathrm{1}−{sinx}\right)^{\mathrm{2}} }\:? \\ $$ Answered by ~blr237~ last updated on 17/Jul/20 $$\:\int\:\frac{\mathrm{1}+\mathrm{2}{sinx}+\left(\mathrm{1}−{cos}^{\mathrm{2}} {x}\right)}{{cos}^{\mathrm{4}} {x}}{dx} \\ $$$$\int\:\left[\:\mathrm{2}\left(\mathrm{1}+{tan}^{\mathrm{2}}…
Question Number 103773 by bemath last updated on 17/Jul/20 $$\int_{{c}} \left(\left({x}^{\mathrm{2}} +\mathrm{2}{xy}^{\mathrm{2}} \right){dx}+\left({x}^{\mathrm{2}} {y}^{\mathrm{2}} −\mathrm{1}\right){dy}\right) \\ $$$${where}\:{C}\:{is}\:{the}\:{boundary}\:{of} \\ $$$${region}\:{define}\:{by}\:{y}^{\mathrm{2}} =\:\mathrm{4}{x}\:{and}\:{y} \\ $$$$=\mathrm{1}\:? \\ $$ Answered…
Question Number 38210 by prof Abdo imad last updated on 22/Jun/18 $${let}\:{f}\left({a}\right)=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{d}\theta}{{a}\:+{sin}^{\mathrm{2}} \theta}\:\:\:\left({a}\:{from}\:{R}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:{g}\left({a}\right)=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{d}\theta}{\left({a}+{sin}^{\mathrm{2}} \theta\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right){calculate}\:\int_{\mathrm{0}}…
Question Number 38211 by prof Abdo imad last updated on 22/Jun/18 $${let}\:{x}>\mathrm{0}\:{and}\:{F}\left({x}\right)=\:\int_{\mathrm{0}} ^{+\infty} \:\frac{{arctan}\left({xt}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{F}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left(\mathrm{2}{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\…
Question Number 38208 by prof Abdo imad last updated on 22/Jun/18 $${let}\:{f}\left({x}\right)={ch}\left(\alpha{x}\right)\: \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}. \\ $$$$\left({f}\:\mathrm{2}\pi\:{periodic}\:{even}\right) \\ $$ Commented by prof Abdo imad last updated…
Question Number 38209 by prof Abdo imad last updated on 22/Jun/18 $${let}\:{f}\left({x}\right)={e}^{−{x}} {cosx} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=−\infty} ^{+\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{1}+{n}^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}}…
Question Number 38207 by prof Abdo imad last updated on 22/Jun/18 $${prove}\:{that}\:{coth}\left({x}\right)−\frac{\mathrm{1}}{{x}}\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} \:+{n}^{\mathrm{2}} \pi^{\mathrm{2}} } \\ $$$$\left({x}\neq\mathrm{0}\right) \\ $$ Commented by math khazana…
Question Number 103742 by mathmax by abdo last updated on 17/Jul/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{\mathrm{dx}}{\left(\mathrm{2x}+\mathrm{1}\right)^{\mathrm{4}} \left(\mathrm{x}+\mathrm{3}\right)^{\mathrm{5}} } \\ $$ Answered by mathmax by abdo last updated…
Question Number 38205 by prof Abdo imad last updated on 22/Jun/18 $${if}\:\:\frac{\mathrm{1}}{{sinx}}\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:{a}_{{n}} {sin}\left({nx}\right)\:\:{find}\:{the}\:{values}\:{of} \\ $$$${a}_{{n}} . \\ $$ Terms of Service Privacy Policy…
Question Number 38204 by prof Abdo imad last updated on 22/Jun/18 $${if}\:\:\frac{\mathrm{1}}{{cosx}}\:=\frac{{a}_{\mathrm{0}} }{\mathrm{2}}\:+\sum_{{n}=\mathrm{1}} ^{\infty} \:{a}_{{n}} {cos}\left({nx}\right) \\ $$$${calculate}\:{a}_{\mathrm{0}} \:{and}\:{a}_{{n}} \\ $$ Commented by math khazana…