Question Number 157099 by mathlove last updated on 19/Oct/21 Commented by yeti123 last updated on 19/Oct/21 $$\int_{\mathrm{2021}} ^{\:\mathrm{2021}} {f}\left({x}\right)\:{dx}\:=\:\mathrm{0} \\ $$ Commented by puissant last…
Question Number 26024 by abdo imad last updated on 17/Dec/17 $$\left.{e}\:{give}\:{a}\:{element}\:{from}\right]\mathrm{0}.\propto\left[\:\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left(\:{ax}^{\mathrm{2}} \right)\right. \\ $$$${and}\:\:\int_{\mathrm{0}} ^{\infty} \:{sin}\left(\:{ax}^{\mathrm{2}} \right){dx}. \\ $$ Terms of Service Privacy…
Question Number 26023 by abdo imad last updated on 17/Dec/17 $${answer}\:{to}\:{question}\mathrm{25980}\:{key}\:{of}\:{slution}\:{we}\:{develop}\:\:{the} \\ $$$${foction}\:{f}\left({x}\right)\:=\:{sin}\left({px}\right)\:{at}\:{fourier}\:{serie}\left(\left({f}\:\mathrm{2}\pi\:{periodic}\right)\right. \\ $$$${f}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{{n}=\propto} \:{a}_{{n}} {sin}\left({nx}\right)\:{and}\:\:{a}_{{n}} =\:\mathrm{2}/{T}\:\int_{\left[{T}\right]} {sin}\left({px}\right){sin}\left({nx}\right){dx}\:\:\:\left({T}=\mathrm{2}\pi\right) \\ $$$$ \\ $$$$ \\…
Question Number 91555 by mr W last updated on 01/May/20 Commented by jagoll last updated on 01/May/20 $${i}\:{forgot}\:{the}\:{section}\:\lfloor{x}\rfloor\: \\ $$ Commented by mathmax by abdo…
Question Number 91542 by jagoll last updated on 01/May/20 $$\int\:\frac{{x}^{\mathrm{3}} }{\mathrm{2}{x}+\mathrm{1}}\:{dx}\:=\:? \\ $$ Commented by Prithwish Sen 1 last updated on 01/May/20 $$\mathrm{put}\:\mathrm{2x}+\mathrm{1}=\frac{\mathrm{1}}{\mathrm{t}}\:\Rightarrow\:\mathrm{dx}\:=\:−\frac{\mathrm{dt}}{\mathrm{2t}^{\mathrm{2}} } \\…
Question Number 91534 by M±th+et+s last updated on 01/May/20 $$\int_{\mathrm{1}} ^{\infty} \frac{{sin}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last updated on 01/May/20…
Question Number 25965 by Chuks” last updated on 17/Dec/17 $${solve}\:{the}\:{integral} \\ $$$$\int\mathrm{sin}^{\mathrm{4}} \theta{d}\theta \\ $$ Answered by $@ty@m last updated on 17/Dec/17 $$\mathrm{sin}\:\mathrm{3}{x}=\mathrm{3sin}\:{x}−\mathrm{4sin}\:^{\mathrm{3}} {x} \\…
Question Number 25960 by abdo imad last updated on 16/Dec/17 $${answer}\:{to}\:\mathrm{25955}.{we}\:{introduce}\:{the}\:{parametric}\:{function} \\ $$$${F}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:{ln}\left(\mathrm{1}+\left(\mathrm{1}+{x}^{\mathrm{2}_{} } \right){t}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{−\mathrm{1}} {dx}\:{after}\:{verifying}\:{that}\: \\ $$$${F}\:{is}\:{derivable}\:{on}\left[\mathrm{0}.\propto\left[\:\:{we}\:{find}\:\:\:\partial{F}/\partial{t}=\:\:\int_{\mathrm{0}} ^{\infty} \left(\:\left(\mathrm{1}+\left(\mathrm{1}+{x}^{\mathrm{2}} \right){t}\right)^{−\mathrm{1}} {dx}\right.\right.\right.…
Question Number 25955 by abdo imad last updated on 16/Dec/17 $$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\int_{\mathrm{0}} ^{\infty} \:\:\boldsymbol{\mathrm{ln}}\left(\mathrm{2}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)\left(\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)^{−\mathrm{1}} \boldsymbol{\mathrm{dx}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 157016 by amin96 last updated on 18/Oct/21 $${f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}^{{x}} }+\frac{\mathrm{1}}{\mathrm{1}+\mathrm{3}^{{x}} }+\frac{\mathrm{1}}{\mathrm{4}^{{x}} +\mathrm{1}}\:\: \\ $$$${find}\:\:\:\int_{\mathrm{1}} ^{\mathrm{5}} {f}\left({x}\right){dx}+\int_{−\mathrm{5}} ^{−\mathrm{1}} {f}\left({x}\right){dx} \\ $$ Answered by amin96 last…