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0-1-x-1-10-x-3-3-dx-

Question Number 163402 by Ahmed777hamouda last updated on 06/Jan/22 $$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\boldsymbol{{x}}−\mathrm{1}\right)^{\mathrm{10}} \left(\boldsymbol{{x}}−\mathrm{3}\right)^{\mathrm{3}} \boldsymbol{{dx}} \\ $$ Answered by Ar Brandon last updated on 06/Jan/22 $${I}=\int_{\mathrm{0}}…

Question-163393

Question Number 163393 by nurtani last updated on 06/Jan/22 Answered by Ar Brandon last updated on 06/Jan/22 $$\left[\frac{\mathrm{1}}{\mathrm{2}}\centerdot\frac{\mathrm{3}}{\mathrm{4}}\left(\mathrm{2}{x}−\mathrm{1}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} −\frac{\mathrm{1}}{\pi}\mathrm{cos}\pi{x}\right]_{\mathrm{1}/\mathrm{2}} ^{\mathrm{1}} \\ $$ Terms of Service…

Question-163368

Question Number 163368 by nurtani last updated on 06/Jan/22 Answered by Ar Brandon last updated on 06/Jan/22 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\frac{\mathrm{4}}{\pi}\mathrm{sin}^{\mathrm{2007}} {x}}{\mathrm{sin}^{\mathrm{2007}} {x}+\mathrm{cos}^{\mathrm{2007}} {x}}{dx}…\left(\mathrm{1}\right) \\ $$$${I}=\int_{\mathrm{0}}…

how-do-i-calculate-for-1-2-

Question Number 163346 by MathsFan last updated on 06/Jan/22 $${how}\:{do}\:{i}\:{calculate}\:{for}\:\frac{\mathrm{1}}{\mathrm{2}}! \\ $$ Commented by Ar Brandon last updated on 06/Jan/22 $$\Gamma\left({x}+\mathrm{1}\right)={x}\Gamma\left({x}\right)={x}\left({x}−\mathrm{1}\right)\Gamma\left({x}−\mathrm{1}\right)…\Gamma\left(\mathrm{1}\right)={x}! \\ $$$$\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=\sqrt{\pi}\:\:,\:\:\Gamma\left(\mathrm{1}\right)=\mathrm{1} \\ $$$$\left(\frac{\mathrm{1}}{\mathrm{2}}\right)!=\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{1}\right)=\frac{\mathrm{1}}{\mathrm{2}}\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=\frac{\sqrt{\pi}}{\mathrm{2}}…