Question Number 200801 by mnjuly1970 last updated on 23/Nov/23 Answered by witcher3 last updated on 24/Nov/23 $$\mathrm{introduce}\:\mathrm{erfc}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\:\sqrt{\pi}}\int_{\mathrm{0}} ^{\mathrm{x}} \mathrm{e}^{−\mathrm{t}^{\mathrm{2}} } \mathrm{dt} \\ $$$$\phi=\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}}…
Question Number 200802 by mnjuly1970 last updated on 23/Nov/23 Answered by witcher3 last updated on 23/Nov/23 $$\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{dx}=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\infty} \mathrm{t}^{\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{1}} \mathrm{e}^{−\mathrm{t}} \mathrm{dt},\mathrm{x}^{\mathrm{2}}…
Question Number 200696 by Bayat last updated on 22/Nov/23 Answered by aleks041103 last updated on 22/Nov/23 $$\left(\mathrm{2}^{{x}} −\mathrm{3}^{{x}} \right)^{\mathrm{2}} =\mathrm{4}^{{x}} +\mathrm{9}^{{x}} −\mathrm{2}.\mathrm{6}^{{x}} =\mathrm{6}^{{x}} −\mathrm{9}^{{x}} \\…
Question Number 200697 by Bayat last updated on 22/Nov/23 Answered by aleks041103 last updated on 22/Nov/23 $${sin}\left(\mathrm{2}{t}\right)=\mathrm{2}{sin}\left({t}\right){cos}\left({t}\right) \\ $$$$\Rightarrow\int\frac{{sin}\left(\mathrm{2}{t}\right)}{\mathrm{2}{sin}\left({t}\right)}{dt}=\int{cos}\left({t}\right){dt}={sin}\left({t}\right)+{C} \\ $$ Terms of Service Privacy…
Question Number 200759 by brahim_mekkaoui last updated on 23/Nov/23 $$\mathrm{let}\:\mathrm{u}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}}{\mathrm{k}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} }\:\mathrm{for}\:\mathrm{n}\in\mathbb{N}_{>\mathrm{0}} \:\: \\ $$$$\mathrm{show}\:\mathrm{that}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}_{>\mathrm{0}} } \mathrm{is}\:\mathrm{increasing}. \\ $$ Terms of…
Question Number 200691 by sonukgindia last updated on 22/Nov/23 Commented by aleks041103 last updated on 22/Nov/23 $${a},{b}\in\mathbb{Z}? \\ $$$${or}\:{just}\:{a},{b}\in\mathbb{R} \\ $$ Answered by witcher3 last…
Question Number 200748 by Rupesh123 last updated on 22/Nov/23 Answered by MM42 last updated on 22/Nov/23 $$\left.{s}=\mathrm{4}\int_{\mathrm{0}} ^{{c}} \left({c}^{\mathrm{2}} −{x}^{\mathrm{2}} \right){dx}=\mathrm{4}\left({c}^{\mathrm{2}} {x}−\frac{\mathrm{1}}{\mathrm{3}}{x}^{\mathrm{3}} \right)\right]_{\mathrm{0}} ^{{c}} \\…
Question Number 200750 by arif1234567890 last updated on 22/Nov/23 $$\mathrm{5}×\mathrm{5} \\ $$$$ \\ $$ Answered by Frix last updated on 22/Nov/23 $$\sqrt{\mathrm{625}} \\ $$ Terms…
Question Number 200746 by sonukgindia last updated on 22/Nov/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 200747 by Rupesh123 last updated on 22/Nov/23 Answered by MM42 last updated on 22/Nov/23 $$\left.{lnx}={u}\Rightarrow\int_{\mathrm{1}} ^{\infty} \:\frac{{du}}{{u}^{\mathrm{2}} }\:=−\frac{\mathrm{1}}{{u}}\right]_{\mathrm{1}} ^{\infty} =\mathrm{1}\:\checkmark \\ $$ Commented…