Question Number 200275 by sonukgindia last updated on 16/Nov/23 Answered by Mathspace last updated on 16/Nov/23 $${I}=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{{dx}}{{a}^{\mathrm{2}} −\mathrm{2}{acosx}+\mathrm{1}}{dx} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{{dx}}{{a}^{\mathrm{2}} −\mathrm{2}{a}\frac{{e}^{{ix}}…
Question Number 200268 by cortano12 last updated on 16/Nov/23 Answered by ajfour last updated on 16/Nov/23 $${D}\:{origin}. \\ $$$${O}_{\mathrm{2}} \equiv\left({s}−{r},\:{s}−{r}\right) \\ $$$${O}_{\mathrm{3}} \equiv\left({r},\:{s}−{r}\right) \\ $$$${let}\:\:{eqn}\:{of}\:{line}\:{DF}\:{be}\:…
Question Number 200270 by ajfour last updated on 16/Nov/23 Commented by mr W last updated on 17/Nov/23 $${i}\:{think}\:{one}\:{vertex}\:{must}\:{lie}\:{at}\:{the} \\ $$$${center}\:{of}\:{a}\:{circle}\:{as}\:{in}\:{diagram}.\:{so} \\ $$$${s}_{{max}} ={radius}=\mathrm{1}. \\ $$…
Question Number 200265 by cherokeesay last updated on 16/Nov/23 Answered by witcher3 last updated on 16/Nov/23 $$\begin{cases}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}\right)^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} −\mathrm{2}.\mathrm{5}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}\right)=\mathrm{0}}\\{\left(\mathrm{2}\right)\Leftrightarrow\left(\mathrm{2}\right)}\end{cases} \\ $$$$\Leftrightarrow\begin{cases}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}−\mathrm{5}\right)^{\mathrm{2}} =\mathrm{0}}\\{\sqrt{\left(\mathrm{x}^{\mathrm{2}}…
Question Number 200262 by sonukgindia last updated on 16/Nov/23 Answered by Frix last updated on 17/Nov/23 $$\mathrm{I}\:\mathrm{get}\:\frac{{a}}{{b}}=−\mathrm{1}+\sqrt{\mathrm{2}+\mathrm{2}\sqrt{\mathrm{2}}}\approx\mathrm{1}.\mathrm{19737} \\ $$ Answered by AST last updated on…
Question Number 200256 by Calculusboy last updated on 16/Nov/23 Commented by Rasheed.Sindhi last updated on 17/Nov/23 $${In}\:{first}\:{sight}\:{your}\:{post}\:{seems} \\ $$$$\left.{to}\:{be}\:{red}\:{flagged}!\::\right) \\ $$ Terms of Service Privacy…
Question Number 200257 by Calculusboy last updated on 16/Nov/23 Answered by witcher3 last updated on 16/Nov/23 $$\mathrm{ln}^{\mathrm{2}} \left(\mathrm{x}\right)+\mathrm{1}=\mathrm{y}\Rightarrow\mathrm{dy}=\mathrm{2}\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}} \\ $$$$=\int\mathrm{y}^{\mathrm{2}} \mathrm{tan}^{−\mathrm{1}} \left(\mathrm{y}\right)\mathrm{dy} \\ $$$$=\frac{\mathrm{y}^{\mathrm{3}} }{\mathrm{3}}\mathrm{tan}^{−\mathrm{1}}…
Question Number 200159 by Calculusboy last updated on 15/Nov/23 Commented by 0670322918 last updated on 15/Nov/23 $$\underset{\mathrm{0}} {\int}^{\mathrm{1}} \frac{{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{3}} +\mathrm{6}{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{1}}{dx}= \\…
Question Number 200186 by Calculusboy last updated on 15/Nov/23 Answered by ajfour last updated on 15/Nov/23 $$\frac{{y}}{{x}}={p}\:,\:\frac{{z}}{{y}}={q}\:,\:\frac{{x}}{{z}}={r}\:=\frac{\mathrm{1}}{{pq}} \\ $$$$\mathrm{1}+{p}+{p}^{\mathrm{2}} =\left(\mathrm{2}+{p}\right)\left(\frac{\mathrm{1}}{{r}}\right)^{\mathrm{2}/\mathrm{3}} \\ $$$$\mathrm{1}+{q}+{q}^{\mathrm{2}} =\left(\mathrm{2}+{q}\right)\left(\frac{\mathrm{1}}{{p}}\right)^{\mathrm{2}/\mathrm{3}} \\ $$$$\mathrm{1}+{r}+{r}^{\mathrm{2}}…
Question Number 200187 by sonukgindia last updated on 15/Nov/23 Answered by Mathspace last updated on 15/Nov/23 $${I}={Re}\left(\int_{−\infty} ^{+\infty} \frac{{e}^{{iax}} }{{x}^{\mathrm{2}} +\mathrm{1}}{dx}\right) \\ $$$${and}\:\int_{−\infty} ^{+\infty} \frac{{e}^{{iax}}…