Menu Close

Category: Integration

C-0-pi-dx-2-cos-2x-

Question Number 165955 by cortano1 last updated on 10/Feb/22 $$\:\:\:\:\mathrm{C}\:=\:\int_{\mathrm{0}} ^{\:\pi} \frac{\mathrm{dx}}{\mathrm{2}+\mathrm{cos}\:\mathrm{2x}}\:=? \\ $$ Answered by MJS_new last updated on 10/Feb/22 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\frac{{dx}}{\mathrm{2}+\mathrm{cos}\:\mathrm{2}{x}}=\mathrm{2}\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}}…

Question-165853

Question Number 165853 by mathlove last updated on 09/Feb/22 Answered by MJS_new last updated on 09/Feb/22 $$\int\frac{\mathrm{2}{x}−\mathrm{1}}{\left({x}+\mathrm{2}\right)^{\mathrm{4}} \left({x}−\mathrm{1}\right)^{\mathrm{4}} }{dx}= \\ $$$$\:\:\:\:\:\left[\mathrm{Ostrogradski}'\mathrm{s}\:\mathrm{Method}\right] \\ $$$$=\frac{\mathrm{40}{x}^{\mathrm{5}} +\mathrm{100}{x}^{\mathrm{4}} −\mathrm{140}{x}^{\mathrm{3}}…

let-B-p-q-0-1-x-p-1-1-x-q-1-dx-calculate-B-1-3-1-3-2-calculate-B-1-2-2-3-

Question Number 34720 by abdo mathsup 649 cc last updated on 10/May/18 $${let}\:{B}\left({p},{q}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{{p}−\mathrm{1}} \left(\mathrm{1}−{x}\right)^{{q}−\mathrm{1}} {dx} \\ $$$${calculate}\:{B}\left(\frac{\mathrm{1}}{\mathrm{3}},\:\frac{\mathrm{1}}{\mathrm{3}}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{B}\left(\frac{\mathrm{1}}{\mathrm{2}}\:,\frac{\mathrm{2}}{\mathrm{3}}\right)\:. \\ $$ Terms of…