Category: Integration

Question Number 133036 by liberty last updated on 18/Feb/21 $${\underset{0}{\int }}^{\frac{\pi }{2}}\frac{dx}{1+\tan {}^{2014}\left(x\right)}=\frac{\pi {\mathrm{e}}^{\mathrm{q}}}{\mathrm{p}}$$$$\mathrm{Find}2\mathrm{p}-\mathrm{q}.$$ Answered by liberty last updated on 18/Feb/21…

Question Number 133027 by Engr_Jidda last updated on 18/Feb/21 $${\stackrel{2}{\int }}_0{x}^5{(8-x^3)}^{\frac{1}{3}}dx$$ Answered by Olaf last updated on 18/Feb/21 $$\Omega\:=\:\int_{\mathrm{0}}…

Question Number 133004 by liberty last updated on 18/Feb/21 $$\mathrm{If}\int \frac{\tan \mathrm{x}}{1+\tan \mathrm{x}+\tan {}^2\mathrm{x}}\mathrm{dx}=\mathrm{x}-\frac{k}{\sqrt{A}}{\tan }^{-1}\left(\frac{k\tan x+1}{\sqrt{A}}\right)+\mathrm{C}$$$$\mathrm{where}\mathrm{C}\mathrm{is}\mathrm{constant}\mathrm{of}\mathrm{integration}.$$$$\mathrm{then}\mathrm{the}\mathrm{ordered}\mathrm{pair}(k,\mathrm{A})\mathrm{is}$$$$\mathrm{equal}\mathrm{to}$$ Answered by EDWIN88 last updated…

Question Number 67466 by ~ À ® @ 237 ~ last updated on 27/Aug/19 $$$$$$$$$$letconsiderforalln⩾1thereal{\left(t\right)}_n=t(t+1)\dots ..(t+n-1)$$$${Find}\:\:\:{L}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left({t}\right)_{\mathrm{1}}…

Question Number 67463 by ~ À ® @ 237 ~ last updated on 27/Aug/19 $$Find$$$$FindK={\int }_0^{\frac{\pi }{2}}\sqrt{tan\theta }d\theta$$ Commented by ~ À…