Question Number 197212 by MathematicalUser2357 last updated on 10/Sep/23 $$\mathrm{Is}\:\int{f}\left({x}\right){dx}=\int_{\mathrm{0}} ^{{x}} \underset{{x}\rightarrow{t}} {\mathrm{lim}}{f}\left({x}\right){dt}? \\ $$ Commented by mahdipoor last updated on 10/Sep/23 $${if}\:\:\:\:\:{limf}\left({x}\right),{x}\rightarrow{t}={f}\left({t}\right) \\ $$$$\int{f}\left({x}\right){dx}=\int_{\mathrm{0}}…
Question Number 197196 by sonukgindia last updated on 10/Sep/23 Answered by mahdipoor last updated on 10/Sep/23 $${blue}\equiv \\ $$$$\pi{r}^{\mathrm{2}} \left(\frac{\alpha_{\mathrm{1}} }{\mathrm{360}}+\frac{\alpha_{\mathrm{2}} }{\mathrm{360}}+\frac{\alpha_{\mathrm{3}} }{\mathrm{360}}…+\frac{\alpha_{{n}} }{\mathrm{360}}\right) \\…
Question Number 197194 by sonukgindia last updated on 10/Sep/23 Answered by witcher3 last updated on 10/Sep/23 $$\mathrm{k}^{\mathrm{1}−\mathrm{n}} +\left(\mathrm{k}+\mathrm{1}\right)^{\mathrm{1}−\mathrm{n}} =\frac{\left(\mathrm{1}+\mathrm{k}\right)^{\mathrm{n}−\mathrm{1}} +\mathrm{k}^{\mathrm{n}−\mathrm{1}} }{\left(\mathrm{k}\left(\mathrm{1}+\mathrm{k}\right)\right)^{\mathrm{n}−\mathrm{1}} } \\ $$$$\Leftrightarrow\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{50}}…
Question Number 197188 by sonukgindia last updated on 10/Sep/23 Answered by witcher3 last updated on 10/Sep/23 $$\mathrm{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(−\mathrm{x}\right)\left(\pi−\mathrm{arcos}\left(\mathrm{x}\right)\right)\mathrm{dx}+\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(\mathrm{x}\right)\mathrm{arccos}\left(\mathrm{x}\right)\mathrm{dx} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{arccos}\left(\mathrm{x}\right)\left(−\mathrm{ln}\left(−\mathrm{x}\right)+\mathrm{ln}\left(\mathrm{x}\right)\right)+\pi\int_{\mathrm{0}}…
Question Number 197190 by universe last updated on 10/Sep/23 $$\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:^{\mathrm{3}} \sqrt{\mathrm{1}−{x}^{\mathrm{7}} }\:{dx}\:−\:\underset{\mathrm{0}} {\int}^{\mathrm{1}} \:^{\mathrm{7}} \sqrt{\mathrm{1}−{x}^{\mathrm{3}} }\:{dx}\:\:=\:\:? \\ $$ Commented by Frix last updated…
Question Number 197191 by tri26112004 last updated on 10/Sep/23 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{3}{x}+\mathrm{7}}{dx} \\ $$ Answered by Frix last updated on 10/Sep/23 $${x}^{\mathrm{3}} −\mathrm{3}{x}+\mathrm{7}=\left({x}−{a}\right)\left({x}^{\mathrm{2}} +{ax}+{b}\right) \\ $$$${a}=−\frac{\sqrt[{\mathrm{3}}]{\mathrm{7}+\mathrm{3}\sqrt{\mathrm{5}}}+\sqrt[{\mathrm{3}}]{\mathrm{7}−\mathrm{3}\sqrt{\mathrm{5}}}}{\:\sqrt[{\mathrm{3}}]{\mathrm{2}}};\:{b}=−\frac{\mathrm{7}}{{a}}…
Question Number 197184 by pete last updated on 10/Sep/23 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{log}\left(−\mathrm{log}{i}\right)=\mathrm{log}\left(\frac{\pi}{\mathrm{2}}\right)−{i}\frac{\pi}{\mathrm{2}} \\ $$ Answered by Frix last updated on 10/Sep/23 $$\mathrm{ln}\:\left(−\mathrm{ln}\:\mathrm{i}\right)\:=\mathrm{ln}\:\frac{\pi}{\mathrm{2}}\:−\mathrm{i}\frac{\pi}{\mathrm{2}} \\ $$$$−\mathrm{ln}\:\mathrm{i}\:=\mathrm{e}^{\mathrm{ln}\:\frac{\pi}{\mathrm{2}}\:−\mathrm{i}\frac{\pi}{\mathrm{2}}} \\ $$$$−\mathrm{ln}\:\mathrm{i}\:=\frac{\pi}{\mathrm{2}}\mathrm{e}^{−\mathrm{i}\frac{\pi}{\mathrm{2}}} \\…
Question Number 197185 by MathematicalUser2357 last updated on 10/Sep/23 $$\mathrm{Simplify} \\ $$$$\sqrt[{\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}}]{\frac{\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{3}}} \centerdot\left(\sqrt{\mathrm{3}}\right)^{\sqrt{\mathrm{2}}} +\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{12}}} }{\left(\sqrt{\mathrm{6}}\right)^{\sqrt{\mathrm{2}}} +\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}} }} \\ $$ Answered by som(math1967) last updated on…
Question Number 197177 by Mathspace last updated on 09/Sep/23 $${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}^{\mathrm{2}} \left({cosx}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 197169 by SANOGO last updated on 09/Sep/23 $$\mathrm{7}{x}+\mathrm{4}{y}=\mathrm{2} \\ $$ Answered by AST last updated on 09/Sep/23 $$\left(\mathrm{2},−\mathrm{3}\right)\:{works}\Rightarrow\left(\mathrm{2}+\mathrm{4}{k},−\mathrm{3}−\mathrm{7}{k}\right)\:{works} \\ $$ Answered by Frix…