Question Number 135495 by greg_ed last updated on 13/Mar/21 $$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{guyz}}\:! \\ $$$$\boldsymbol{\mathrm{let}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{try}}\:\boldsymbol{\mathrm{this}}\::\:\boldsymbol{\mathrm{I}}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\boldsymbol{{sin}}^{\mathrm{2}} \boldsymbol{{x}}}{\boldsymbol{{cos}}^{\mathrm{3}} \boldsymbol{{x}}}\boldsymbol{{dx}}. \\ $$ Answered by mathmax by abdo last updated…
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Question Number 4344 by Filup last updated on 12/Jan/16 $$\mathrm{for}\:\int{f}\left({x}\right){dx}={F}\left({x}\right)+{c} \\ $$$$\mathrm{and}\:{sgn}\left({x}\right)=\frac{{x}}{\mid{x}\mid}=\frac{\mid{x}\mid}{{x}}\:\:\:\forall{x}\neq\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{let}\:\mathrm{sgn}\left({x}\right)=\mathrm{0}\:\mathrm{for}\:{x}=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{does}\: \\ $$$$\int{sgn}\left({f}\left({x}\right)\right){f}\left({x}\right){dx}={sgn}\left({f}\left({x}\right)\right)\int{f}\left({x}\right){dx} \\ $$$$\because{sgn}\left({f}\left({x}\right)\right)\:\mathrm{is}\:\mathrm{just}\:\mathrm{a}\:\mathrm{constant}\:\pm\mathrm{1}\:\mathrm{or}\:\mathrm{0}. \\ $$ Commented…
Question Number 135389 by Bird last updated on 12/Mar/21 $${let}\:{U}_{{n}} =\int_{−\infty} ^{\infty} \:\:\frac{{cos}\left({nx}\right)}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$${calculate}\:{lim}_{{n}\rightarrow\infty} {e}^{{n}^{\mathrm{2}} } {U}_{{n}} \\ $$ Terms of Service…
Question Number 4314 by Filup last updated on 09/Jan/16 $${S}=\int_{{a}} ^{\:{b}} {n}^{{t}^{\mathrm{2}} } {dt} \\ $$$${n}\in\mathbb{R} \\ $$$$ \\ $$$$\mathrm{Can}\:\mathrm{we}\:\mathrm{solve}\:{S}? \\ $$ Commented by Filup…
Question Number 135382 by Bird last updated on 12/Mar/21 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} {ln}\left(\mathrm{1}−{x}^{\mathrm{4}} \right){dx}\:{with}\:{n} \\ $$$${integr}\:{natural} \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 135372 by Bird last updated on 12/Mar/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left(\sqrt{{x}}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{\mathrm{3}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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} \\ $$$${assumed}\:{finite}\:{for}\:{T}\:{being}\:{a}\: \\ $$$${positive}\:{constant},\:{and}\:{Q}\:{taking}\:{the} \\ $$$${form}\:{Q}={KT}^{{n}} \:,{where}\:{K}={constant} \\ $$$${and}\:{n}\in\mathbb{Z}. \\ $$$$…
Question Number 135361 by leena12345 last updated on 12/Mar/21 $${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…