Category: Vector

Question Number 197550 by Erico last updated on 21/Sep/23 $$\mathrm{Calcul}\mathrm{I}={\underset{0}{\int }}^{\frac{\pi }{2}}\frac{\ln \left(\mathrm{cost}\right)}{1+{\sin }^2\mathrm{t}}\mathrm{dt}$$ Answered by qaz last updated on 22/Sep/23 $${I}=\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{{ln}\mathrm{cos}\:{t}}{\mathrm{2}−\mathrm{cos}\:^{\mathrm{2}}…

Question Number 196145 by Erico last updated on 18/Aug/23 $$\mathrm{Calculer}{\underset{\frac{1}{\alpha }}{\int }}^{+\mathrm{\infty }}{e}^{-\alpha t^2+2t}dt$$ Answered by Mathspace last updated on 20/Aug/23 $${t}=\frac{\mathrm{1}}{\alpha}+{x}\:\Rightarrow \…

Question Number 195165 by Nimnim111118 last updated on 25/Jul/23 $$\mathrm{If}\overrightarrow{{\mathrm{r}}_1}=(\sin \theta ,\cos \theta ,\theta ),\overrightarrow{{\mathrm{r}}_2}=(\cos \theta ,-\sin \theta ,-3)\mathrm{and}$$$$\:\overset{\rightarrow} {\mathrm{r}_{\mathrm{3}} }=\left(\mathrm{2},\mathrm{3},−\mathrm{1}\right),\:\mathrm{find}\:\frac{\mathrm{d}}{\mathrm{d}\theta}\left\{\overset{\rightarrow} {\mathrm{r}_{\mathrm{1}} }×\left(\overset{\rightarrow} {\mathrm{r}_{\mathrm{2}} }×\overset{\rightarrow} {\mathrm{r}_{\mathrm{3}} }\right)\right\}\:\mathrm{at}\:\theta=\mathrm{0} \…

Question Number 194600 by byaw last updated on 10/Jul/23 $$$$An object is pulled up a smooth plane inclined at angle 45° to the…

Question Number 194497 by Biteshwar last updated on 08/Jul/23 $$12\mathrm{th}$$$$$$$$$$$$$$$$$$ Commented by Frix last updated…