Category: Integration

Question Number 45885 by Meritguide1234 last updated on 17/Oct/18 Commented by maxmathsup by imad last updated on 18/Oct/18 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{n}\left(\mathrm{1}−\left({sinx}\right)^{\frac{\mathrm{1}}{{n}}} \right){dx}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:{f}_{{n}}…

Question Number 45836 by  last updated on 17/Oct/18 $$\int\frac{\mathrm{1}}{{sin}^{\mathrm{2}} {x}}\centerdot\frac{\mathrm{1}}{\left(\mathrm{3}+\mathrm{2}{cosx}\right)}{dx}=? \\ $$ Commented by MJS last updated on 17/Oct/18 $$\mathrm{you}'\mathrm{re}\:\mathrm{welcome} \\ $$ Commented by…

Question Number 45802 by MJS last updated on 17/Oct/18 $$\mathrm{some}\:\mathrm{practice}\:\mathrm{for}\:\mathrm{the}\:\mathrm{brave}… \\ $$$$\int\frac{\mathrm{cos}^{\mathrm{2}} \:{x}\:\mathrm{sin}^{\mathrm{2}} \:{x}}{\mathrm{cos}\:{x}\:+\mathrm{sin}\:{x}}{dx}=? \\ $$$$\int\frac{\mathrm{cos}^{\mathrm{2}} \:{x}\:\mathrm{tan}^{\mathrm{2}} \:{x}}{\mathrm{cos}\:{x}\:+\mathrm{tan}\:{x}}{dx}=? \\ $$$$\int\frac{\mathrm{sin}^{\mathrm{2}} \:{x}\:\mathrm{tan}^{\mathrm{2}} \:{x}}{\mathrm{sin}\:{x}\:+\mathrm{tan}\:{x}}{dx}=? \\ $$ Commented…

Question Number 45771 by maxmathsup by imad last updated on 16/Oct/18 $${find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}+{t}^{\mathrm{2}} \right){dtand}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}+{t}^{\mathrm{2}} \right){dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{f}^{'} \left({x}\right)\:{and}\:{g}^{'} \left({x}\right). \\ $$ Answered…

Question Number 45721 by Necxx last updated on 15/Oct/18 $$\:{Integrate}\:\mathrm{sin}\:\left({x}^{\mathrm{2}} \right){dx} \\ $$ Commented by MJS last updated on 16/Oct/18 $$\mathrm{not}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{resolve}\:\mathrm{to}\:\mathrm{elementary}\:\mathrm{function} \\ $$ Commented by…