Question Number 163368 by nurtani last updated on 06/Jan/22 Answered by Ar Brandon last updated on 06/Jan/22 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\frac{\mathrm{4}}{\pi}\mathrm{sin}^{\mathrm{2007}} {x}}{\mathrm{sin}^{\mathrm{2007}} {x}+\mathrm{cos}^{\mathrm{2007}} {x}}{dx}…\left(\mathrm{1}\right) \\ $$$${I}=\int_{\mathrm{0}}…
Question Number 97827 by amrabdelsabour last updated on 10/Jun/20 Commented by Rio Michael last updated on 10/Jun/20 $$\mathrm{Any}\:\mathrm{ideas}\:\mathrm{what}\:\mathrm{this}\:\mathrm{means}? \\ $$ Terms of Service Privacy Policy…
Question Number 163346 by MathsFan last updated on 06/Jan/22 $${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}! \\ $$$$\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=\sqrt{\pi}\:\:,\:\:\Gamma\left(\mathrm{1}\right)=\mathrm{1} \\ $$$$\left(\frac{\mathrm{1}}{\mathrm{2}}\right)!=\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{1}\right)=\frac{\mathrm{1}}{\mathrm{2}}\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=\frac{\sqrt{\pi}}{\mathrm{2}}…
Question Number 163333 by MathsFan last updated on 06/Jan/22 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\sqrt{{sinx}}}{\:\sqrt{{sinx}}+\sqrt{{cosx}}}{dx} \\ $$ Commented by smallEinstein last updated on 06/Jan/22 Commented by MathsFan last…
Question Number 163324 by ZiYangLee last updated on 06/Jan/22 $$\mathrm{Given}\:\mathrm{that}\:\left\{{a}_{{n}} \right\}\:\mathrm{is}\:\mathrm{a}\:\mathrm{geometric}\:\mathrm{sequence} \\ $$$$\mathrm{where}\:\mathrm{the}\:\mathrm{first}\:\mathrm{term},\:{a}_{\mathrm{1}} >\mathrm{1}\:\mathrm{and}\:\mathrm{the}\:\mathrm{common} \\ $$$$\mathrm{ratio},\:{r}>\mathrm{0}.\: \\ $$$$\mathrm{If}\:{b}_{{n}} =\mathrm{log}_{\mathrm{2}} \:{a}_{{n}} \:\mathrm{where}\:{n}\in\mathbb{N},\:{b}_{\mathrm{1}} +{b}_{\mathrm{3}} +{b}_{\mathrm{5}} =\mathrm{6}, \\…
Question Number 163323 by ZiYangLee last updated on 06/Jan/22 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{equation} \\ $$$$\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}=\mathrm{0}\:\mathrm{are}\:\alpha\:\mathrm{and}\:\beta.\:\: \\ $$$${f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{function}\:\mathrm{where}\:{f}\left(\alpha\right)=\beta\:, \\ $$$${f}\left(\beta\right)=\alpha\:\mathrm{and}\:{f}\left(\mathrm{0}\right)=\mathrm{6}\:.\: \\ $$$$\mathrm{Find}\:{f}\left({x}\right). \\ $$ Commented by cortano1 last…
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Question Number 163318 by KONE last updated on 06/Jan/22 Answered by Mathspace last updated on 06/Jan/22 $$={lim}_{{n}\rightarrow\infty} \frac{\mathrm{1}}{{n}}\sum_{{k}=\mathrm{1}} ^{{n}} \left[{e}^{\frac{{k}}{{n}}} \right] \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}} \left[{e}^{{x}}…
Question Number 163316 by SANOGO last updated on 06/Jan/22 $${calculer}\:{une}\:{primitive}\:{de}\:{x}:\rightarrow{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right) \\ $$$${puis}\:{jusrifier}\:{la}\:{convergence}\:{de}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx} \\ $$ Answered by amin96 last updated…
Question Number 32241 by mondodotto@gmail.com last updated on 22/Mar/18 Commented by MJS last updated on 22/Mar/18 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{that}'\mathrm{s}\:\mathrm{true}\:\mathrm{if}\:\mathrm{you} \\ $$$$\mathrm{can}\:\mathrm{freely}\:\mathrm{choose}\:{a},\:{b}\:\mathrm{and}\:\theta \\ $$$$\mathrm{but}\:\mathrm{of}\:\mathrm{course}\:\mathrm{you}\:\mathrm{can}\:\mathrm{find}\:\theta \\ $$$$\mathrm{for}\:\mathrm{any}\:\mathrm{given}\:\mathrm{triplet}\:{a},\:{b},\:{c}\:\:\mathrm{with} \\ $$$$\mathrm{or}\:\mathrm{without}\:{a}^{\mathrm{2}}…