Category: Integration

Question Number 101531 by mhmd last updated on 03/Jul/20 $$find\int \sqrt{ax-x^2}dx$$ Answered by Mr.D.N. last updated on 03/Jul/20 $$\mathrm{I}=\int \sqrt{\mathrm{ax}-{\mathrm{x}}^2}\mathrm{dx}$$$$\:\:\:=\:\int\sqrt{−\left(\mathrm{x}^{\mathrm{2}} −\mathrm{ax}\right)}\:\:\:\mathrm{dx}…

Question Number 35990 by abdo mathsup 649 cc last updated on 26/May/18 $$calculate{\int }_2^5\frac{xdx}{2x+1+\sqrt{x-1}}$$ Commented by abdo mathsup 649 cc last updated…

Question Number 35982 by abdo mathsup 649 cc last updated on 26/May/18 $$letf\left(t\right)={\int }_0^{\mathrm{\infty }}{e}^{-arctsn(1+{tx}^2)}dxwithtfromR$$$$1)calculate{f}^{{}^{\prime }}\left(t\right)$$$$2)findasimpleformoff\left(t\right).$$ Terms…

Question Number 167040 by cortano1 last updated on 05/Mar/22 $${\int }_0^{\frac{\pi }{2}}\frac{1}{1+\sin {}^6\mathrm{x}}\mathrm{dx}=?$$ Commented by greogoury55 last updated on 05/Mar/22 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sec}\:^{\mathrm{6}}…

Question Number 101493 by bemath last updated on 03/Jul/20 $$\int \sqrt{\mathrm{x}.\sqrt[3]{\mathrm{x}.\sqrt[4]{\mathrm{x}.\sqrt[5]{\mathrm{x}.\sqrt[6]{\mathrm{x}.\sqrt[7]{\mathrm{x}\dots }}}}}}\mathrm{dx}=$$$$$$ Answered by floor(10²Eta[1]) last updated on 03/Jul/20 $${let}^{\prime }sseeasmallcasefirsttounderstand$$$${better}\:{whats}\:{going}\:{on} \…