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by-use-Gamma-function-prove-1-0-pi-8-cos-3-4xdx-1-6-2-0-pi-sin-6-x-2-cos-8-x-2-dx-5pi-2-11-

Question Number 139371 by mohammad17 last updated on 26/Apr/21 $${by}\:{use}\:{Gamma}\:{function}\:{prove}\: \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{8}}} {cos}^{\mathrm{3}} \mathrm{4}{xdx}=\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:\int_{\mathrm{0}} ^{\:\pi} {sin}^{\mathrm{6}} \left(\frac{{x}}{\mathrm{2}}\right){cos}^{\mathrm{8}} \left(\frac{{x}}{\mathrm{2}}\right){dx}=\frac{\mathrm{5}\pi}{\mathrm{2}^{\mathrm{11}}…

Question-8259

Question Number 8259 by 314159 last updated on 04/Oct/16 Answered by Yozzias last updated on 04/Oct/16 $$\mathrm{Let}\:\mathrm{u}\left(\mathrm{x}\right)=\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{n}} \:\:\left(\mathrm{n}\in\mathbb{N},\mathrm{n}\geqslant\mathrm{2}\right) \\ $$$$\mathrm{2}^{\mathrm{n}} −\mathrm{1}=\mathrm{C}_{\mathrm{1}} +\mathrm{C}_{\mathrm{2}} +\mathrm{C}_{\mathrm{3}} +\mathrm{C}_{\mathrm{4}} +…+\mathrm{C}_{\mathrm{n}}…

x-1-lt-2-x-3-

Question Number 8262 by 666225 last updated on 04/Oct/16 $$\mid{x}−\mathrm{1}\mid\:<\:\mathrm{2}\:\Rightarrow\:\mid{x}−\mathrm{3}\mid \\ $$ Commented by 123456 last updated on 04/Oct/16 $$\mid{x}−\mathrm{1}\mid<\mathrm{2}\Leftrightarrow−\mathrm{2}<{x}−\mathrm{1}<\mathrm{2} \\ $$$$−\mathrm{2}−\mathrm{2}<{x}−\mathrm{3}<\mathrm{2}−\mathrm{2} \\ $$$$−\mathrm{4}<{x}−\mathrm{3}<\mathrm{0} \\…

x-y-3-and-x-5-y-3-5-find-x-and-y-

Question Number 139331 by 7770 last updated on 26/Apr/21 $$\sqrt{\boldsymbol{{x}}}+\sqrt{\boldsymbol{{y}}}=\mathrm{3}\:\:\boldsymbol{{and}} \\ $$$$\sqrt{\boldsymbol{{x}}+\mathrm{5}}+\sqrt{\boldsymbol{{y}}+\mathrm{3}}=\mathrm{5} \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{x}}\:\boldsymbol{{and}}\:\boldsymbol{{y}} \\ $$ Answered by bemath last updated on 26/Apr/21 $$\left(\mathrm{1}\right)\mathrm{x}=\mathrm{9}+\mathrm{y}−\mathrm{6}\sqrt{\mathrm{y}}\: \\…

Question-73789

Question Number 73789 by liki last updated on 15/Nov/19 Commented by liki last updated on 15/Nov/19 $$..{Sory}\:{sir};\:{Mr}\:{mind}\:{is}\:{power}\:{plz}\:{help}\: \\ $$$$\:\:{that}\:{qn}\:\mathrm{5}\:\left({a}\right),\left({b}\right),\left({c}\right)\:{and}\:\left({d}\right).\:{or}\:{anyone} \\ $$$$\:{to}\:{assist}\:{me}\:{this}\:{qn} \\ $$ Commented by…