Question Number 758 by 13/NaSaNa(N)056565 last updated on 08/Mar/15 $$\int{x}\mathrm{tan}^{−\mathrm{1}} {xdx} \\ $$$$ \\ $$ Commented by malwaan last updated on 08/Mar/15 $${integral}\:{by}\:{parts} \\ $$$$\int{udv}={uv}−\int{vdu}\:…
Question Number 131820 by mr W last updated on 09/Feb/21 Commented by liberty last updated on 09/Feb/21 $$\frac{\mathrm{x}}{\mathrm{2}}=\:\frac{\mathrm{3}}{\mathrm{1}}\Rightarrow\mathrm{x}=\mathrm{6} \\ $$$$\mathrm{x}.\mathrm{1}\:=\:\mathrm{2}.\mathrm{3}\:\Rightarrow\mathrm{x}=\mathrm{6} \\ $$$$\frac{\mathrm{3}}{\mathrm{x}}=\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow\mathrm{x}=\mathrm{6} \\ $$ Commented…
Question Number 737 by 123456 last updated on 08/Mar/15 $$\frac{\mathrm{1}}{{T}}\underset{{t}_{\mathrm{1}} } {\overset{{t}_{\mathrm{2}} } {\int}}{V}\mathrm{sin}\:\omega{t}−{V}_{\gamma} \:{dt}=? \\ $$$${t}_{\mathrm{1}} \:{and}\:{t}_{\mathrm{2}} \:{are}\:{solution}\:{to} \\ $$$${V}\mathrm{sin}\:\omega{t}={V}_{\gamma} \\ $$$${V}\geqslant{V}_{\gamma} \\ $$$${V}_{\gamma}…
Question Number 66211 by mr W last updated on 10/Aug/19 Commented by mr W last updated on 10/Aug/19 $${Find}\:{the}\:{maximum}\:{area}\:{of}\:{a}\:{right} \\ $$$${triangle}\:{inscribed}\:{in}\:{an}\:{ellipse}. \\ $$ Commented by…
Question Number 652 by 123456 last updated on 19/Feb/15 $${if}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:{is}\:{continuous}\:{and} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right)+{y} \\ $$$$\mathrm{1}.\:{find}\:{f}\left({x}\right) \\ $$$$\mathrm{2}.\:{proof}\:{or}\:{disproof}\:{that}\:{f}'\left({x}\right)=\mathrm{1} \\ $$$$\mathrm{3}.\:{if}\:{f}\left(\mathrm{0}\right)=\mathrm{0}\:{proof}\:{or}\:{disproof}\:{that}\:{f}\left({x}\right)={x} \\ $$ Answered by prakash jain last…
Question Number 650 by 123456 last updated on 19/Feb/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right){g}\left({y}\right) \\ $$$${g}\left({x}+{y}\right)={f}\left({x}\right){g}\left({x}\right)+{g}\left({y}\right) \\ $$ Answered by prakash jain last updated on…
Question Number 630 by 123456 last updated on 15/Feb/15 $$\underset{−\frac{\pi}{\mathrm{2}}} {\overset{+\frac{\pi}{\mathrm{2}}} {\int}}\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}{dx} \\ $$$$\underset{−\frac{\pi}{\mathrm{2}}} {\overset{+\frac{\pi}{\mathrm{2}}} {\int}}\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}\mathrm{cos}\left(\mathrm{2}{nx}\right){dx} \\ $$$$\underset{−\frac{\pi}{\mathrm{2}}} {\overset{+\frac{\pi}{\mathrm{2}}} {\int}}\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}\mathrm{sin}\left(\mathrm{2}{nx}\right){dx} \\ $$$${n}\in\mathbb{N}^{\ast} \\ $$ Commented…
Question Number 66109 by Rio Michael last updated on 09/Aug/19 Commented by Rio Michael last updated on 09/Aug/19 $${The}\:{diagram}\:{above}\:{shows}\:{a}\:{uniform}\:{semi}−{circular}\:{lamina}\:{of}\:{radius}\:\mathrm{2}{a} \\ $$$$,{center}\:{O}.\:{The}\:{distance}\:{of}\:{the}\:{centre}\:{of}\:{mass}\:{form}\:{P},\:{vertically}\:{above}\:{O}\:{is} \\ $$$$ \\ $$$${A}\:\:\frac{\mathrm{6}{a}\pi−\mathrm{8}{a}}{\mathrm{3}\pi}…
Question Number 131624 by mr W last updated on 06/Feb/21 Commented by mr W last updated on 06/Feb/21 $${an}\:{old}\:{unsolved}\:{question} \\ $$ Commented by MJS_new last…
Question Number 516 by 112358 last updated on 25/Jan/15 $${Find}\:{all}\:{triangles}\:{with}\:{consecutive} \\ $$$${integer}\:{sides}\:{and}\:{having}\:{an}\:{angle}\:{twice} \\ $$$${another}\:{angle}. \\ $$ Commented by prakash jain last updated on 22/Jan/15 $${a}={n}…