Question Number 208354 by kgmxdd last updated on 13/Jun/24 Commented by Frix last updated on 13/Jun/24 $$=\frac{\mathrm{4}}{\pi}!!! \\ $$$$\left(\mathrm{I}\:\mathrm{found}\:\mathrm{this}\:\mathrm{online}.\right) \\ $$ Terms of Service Privacy…
Question Number 208332 by essaad last updated on 12/Jun/24 Answered by Frix last updated on 12/Jun/24 $$\underset{{k}=\mathrm{0}} {\overset{{n}} {\prod}}\:\left({k}+{a}\right)\:={a}\left({a}+\mathrm{1}\right)\left({a}+\mathrm{2}\right)…\left({a}+{n}\right)=\frac{\left({a}+{n}\right)!}{\left({a}−\mathrm{1}\right)!} \\ $$$$\Rightarrow \\ $$$$\underset{{k}=\mathrm{0}} {\overset{{n}} {\prod}}\:\frac{{k}^{\mathrm{2}}…
Question Number 208334 by Shrodinger last updated on 12/Jun/24 $$\int_{\mathrm{0}} ^{\frac{\mathrm{4}}{\pi}} {ln}\left({cosx}\right){dx} \\ $$ Commented by Frix last updated on 12/Jun/24 $$\mathrm{This}\:\mathrm{question}\:\mathrm{has}\:\mathrm{been}\:\mathrm{answered}\:\left(\mathrm{208280}\right) \\ $$ Terms…
Question Number 208335 by Shrodinger last updated on 12/Jun/24 $$\int_{−\mathrm{1}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{t}^{\mathrm{4}} }{dt} \\ $$ Answered by Frix last updated on 12/Jun/24 $$\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\sqrt{\mathrm{1}−{t}^{\mathrm{4}}…
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Question Number 208327 by efronzo1 last updated on 12/Jun/24 Answered by A5T last updated on 12/Jun/24 $${DE}=\mathrm{5}{x},{DF}=\mathrm{12}{x} \\ $$$${Let}\:{the}\:{perpendicular}\:{from}\:{A}\:{to}\:{BC}\:{meet}\:{it}\:{at}\:{H}; \\ $$$${AH}×{BC}=\mathrm{3}×\mathrm{4}=\mathrm{12}\Rightarrow{AH}=\frac{\mathrm{12}}{\mathrm{5}} \\ $$$$\Rightarrow{BH}=\sqrt{\mathrm{9}−\frac{\mathrm{144}}{\mathrm{25}}}=\frac{\mathrm{9}}{\mathrm{5}} \\ $$$$\frac{{AD}}{{AB}}=\frac{{DE}}{{BC}}={x}\Rightarrow{AD}=\mathrm{3}{x}\Rightarrow{AE}=\mathrm{4}{x}…
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Question Number 208316 by Tawa11 last updated on 11/Jun/24 $$\int\:\frac{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{3}}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}\:\:+\:\:\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Answered by Frix last updated on 11/Jun/24 $$\int\frac{{x}^{\mathrm{2}} +\mathrm{3}}{{x}^{\mathrm{2}}…
Question Number 208318 by SANOGO last updated on 11/Jun/24 $${calcul}\:\:\:{lim}\:{n}\rightarrow+\infty \\ $$$$\int_{\mathrm{0}} ^{+\infty} \:\frac{{cos}\left({nx}\right)}{\left({nx}+\mathrm{1}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\:}{dx} \\ $$ Answered by Berbere last updated on 11/Jun/24 $$\mid\int_{\mathrm{0}}…
Question Number 208312 by messele last updated on 11/Jun/24 $${lim}_{{x}\rightarrow\mathrm{0}\:\frac{{a}^{{x}} −\mathrm{1}}{{x}}\:=\:{log}\:{a}} \\ $$ Answered by mathzup last updated on 11/Jun/24 $${let}\:{f}\left({x}\right)={a}^{{x}} \:={e}^{{xlna}} \:\Rightarrow{f}\left(\mathrm{0}\right)=\mathrm{1}\:{and} \\ $$$${lim}_{{x}\rightarrow\mathrm{0}}…