Question Number 11517 by Joel576 last updated on 27/Mar/17 $${f}\::\:\mathbb{R}\:\rightarrow\:\mathbb{R} \\ $$$$\mathrm{If}\:\:{x}^{\mathrm{2}} {f}\left({x}\right)\:+\:{f}\left(\mathrm{1}−{x}\right)\:=\:\mathrm{2}{x}\:−\:{x}^{\mathrm{4}} \\ $$$$\mathrm{Determine}\:{f}\left({x}\right) \\ $$ Answered by sma3l2996 last updated on 27/Mar/17 $${let}\:{u}=\mathrm{1}−{x}…
Question Number 142429 by Mathspace last updated on 31/May/21 $${calculate}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{{log}^{{n}} {x}}{\mathrm{1}+{x}^{{n}} }{dx} \\ $$$${find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma{U}_{{n}} \\ $$ Answered by mathmax by abdo last…
Question Number 142425 by Mathspace last updated on 31/May/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{log}^{\mathrm{3}} {x}}{\mathrm{1}+{x}^{\mathrm{3}} }{dx} \\ $$ Answered by mathmax by abdo last updated on 02/Jun/21…
Question Number 142430 by Mathspace last updated on 31/May/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{log}^{\mathrm{2}} {x}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 31/May/21 $$\int_{\mathrm{0}}…
Question Number 142424 by Mathspace last updated on 31/May/21 $$\left.\mathrm{2}\right){calculate}\:\sum_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \:{sin}\left(\frac{{k}\pi}{{n}}\right)\:\:\:\left({n}>\mathrm{2}\right) \\ $$$$\left.\mathrm{1}\right)\:{use}\:{Rieman}\:{sum}\:{to}\:{prove} \\ $$$${that}\:\int_{\mathrm{0}} ^{\pi} {log}\left({sinx}\right){dx}=−\pi{log}\mathrm{2} \\ $$ Terms of Service Privacy Policy…
Question Number 142426 by Mathspace last updated on 31/May/21 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{xlogx}}{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{\mathrm{2}} }{dx} \\ $$ Answered by mindispower last updated on 01/Jun/21 $${x}\rightarrow\frac{\mathrm{1}}{{x}} \\…
Question Number 142423 by Mathspace last updated on 31/May/21 $${study}\:{the}\:{convergence}\:{of} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{{log}^{\mathrm{2}} {x}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 142389 by alcohol last updated on 31/May/21 $$\int\frac{{e}^{{x}} }{{cosx}}{dx} \\ $$ Answered by ArielVyny last updated on 31/May/21 $$=\left[{e}^{{x}} ×\frac{\mathrm{1}}{{cosx}}\right]−\int{e}^{{x}} ×−\frac{{sinx}}{{cos}^{\mathrm{2}} {x}}{dx} \\…
Question Number 142365 by mathmax by abdo last updated on 30/May/21 $$\mathrm{calculate}\:\int\:\:\sqrt{\mathrm{1}+\mathrm{e}^{\mathrm{x}} \:+\mathrm{e}^{\mathrm{2x}} }\mathrm{dx} \\ $$ Answered by MJS_new last updated on 05/Jun/21 $$\int\sqrt{\mathrm{e}^{\mathrm{2}{x}} +\mathrm{e}^{{x}}…
Question Number 11299 by agni5 last updated on 19/Mar/17 $$\mathrm{Define}\:\mathrm{two}\:\mathrm{partition}\:\mathrm{p}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{p}_{\mathrm{2}} \:\mathrm{of}\:\left[\mathrm{2},\mathrm{5}\right]\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{p}_{\mathrm{1}} \subset\mathrm{p}_{\mathrm{2}} \:.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{upper}\:\mathrm{and}\:\mathrm{lower}\:\mathrm{product} \\ $$$$\mathrm{sums}\:\mathrm{with}\:\mathrm{respet}\:\mathrm{to}\:\mathrm{f}\:,?\mathrm{defined}\:\mathrm{by} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}\:,\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}<\mathrm{4} \\ $$$$\:\:\:\:\:\:\:\:=\mathrm{1}−\mathrm{x}^{\mathrm{2}} \:,\:\:\:\:\:\mathrm{x}\:\geqslant\mathrm{4}\:\:. \\ $$$$\mathrm{Also}\:\mathrm{verify}\:\mathrm{the}\:\mathrm{relationship}\:\mathrm{between}\:\mathrm{these}…