Question Number 6390 by FilupSmith last updated on 25/Jun/16 $$\mathrm{Solve}: \\ $$$${I}\left({n}\right)=\int_{\mathrm{0}} ^{\:{n}} \left(−\mathrm{1}\right)^{\lfloor{x}\rfloor} {x}^{\mathrm{2}} {dx} \\ $$ Commented by prakash jain last updated on…
Question Number 71925 by Henri Boucatchou last updated on 22/Oct/19 $$\:\boldsymbol{{Solve}}\:\:\sqrt{\mathrm{1}\:−\:\boldsymbol{{x}}^{\mathrm{2}} }\:=\:\boldsymbol{{x}}^{\mathrm{4}/\mathrm{3}} \\ $$ Answered by MJS last updated on 23/Oct/19 $${x}={t}^{\mathrm{3}/\mathrm{2}} \\ $$$$\sqrt{\mathrm{1}−{t}^{\mathrm{3}} }={t}^{\mathrm{2}}…
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Question Number 6384 by Rasheed Soomro last updated on 25/Jun/16 Commented by Rasheed Soomro last updated on 25/Jun/16 $${Question}\:{reposted}. \\ $$ Commented by nburiburu last…
Question Number 71918 by lalitchand last updated on 22/Oct/19 $$\mathrm{If}\:\mathrm{Cos}\theta=\frac{\mathrm{x}\:\mathrm{cos}\beta\:−\:\mathrm{y}}{\mathrm{x}\:−\:\mathrm{y}\:\mathrm{cos}\beta}\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that},\:\mathrm{tan}\frac{\theta}{\mathrm{2}}\:=\sqrt{\frac{\mathrm{x}−\mathrm{y}}{\mathrm{x}+\mathrm{y}}\:}\:\mathrm{tan}\frac{\beta}{\mathrm{2}} \\ $$ Commented by Prithwish sen last updated on 22/Oct/19 $$\mathrm{Using}\:\mathrm{componendo}\:\mathrm{dividendo} \\ $$$$\frac{\mathrm{1}−\mathrm{cos}\theta}{\mathrm{1}+\mathrm{cos}\theta}\:=\:\frac{\left(\mathrm{1}−\mathrm{cos}\beta\right)\left(\mathrm{x}+\mathrm{y}\right)}{\left(\mathrm{1}+\mathrm{cos}\beta\right)\left(\mathrm{x}−\mathrm{y}\right)} \\ $$$$\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\theta}}{\mathrm{2}}\:=\:\sqrt{\frac{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{y}}}}\:\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\beta}}{\mathrm{2}}…
Question Number 137448 by liberty last updated on 03/Apr/21 $$\int_{\mathrm{0}} ^{\:\mathrm{3}/\mathrm{4}} \frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:? \\ $$ Answered by MJS_new last updated on 03/Apr/21 $$\int\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}= \\…
Question Number 6374 by sanusihammed last updated on 25/Jun/16 $${Show}\:{that} \\ $$$$\overset{−} {{a}}\:×\:\left({b}\:×\:{c}\right)\:=\:\left(\overset{−} {{a}}\:.\:\overset{−} {{c}}\right)\overset{−} {{b}}\:\:−\:\:\left(\overset{−} {{a}}\:.\:\overset{−} {{b}}\right)\overset{−} {{c}} \\ $$ Commented by FilupSmith last…
Question Number 6373 by sanusihammed last updated on 25/Jun/16 $${If}\:\:\:\:\mathrm{9}{log}_{{a}} ^{\mathrm{5}} \:\:=\:\:{log}_{\mathrm{5}} ^{{a}} \\ $$$${find}\:{the}\:{value}\:{of}\:{a}\: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{SOLUTION} \\ $$$$ \\ $$$$\mathrm{9}{log}_{{a}} ^{\mathrm{5}} \:\:=\:\:{log}_{\mathrm{5}}…
Question Number 6370 by sanusihammed last updated on 25/Jun/16 $${If}\:\:{x}\:=\:\frac{\mathrm{3}{sin}\theta}{\:\sqrt{{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:}}\:\:\:{and}\:\:{y}\:=\:\mathrm{4}{cos}\theta \\ $$$${find}\:\:{cos}\theta \\ $$ Commented by nburiburu last updated on 25/Jun/16 $${cos}\theta={y}/\mathrm{4}\:{with}\:\mathrm{16}{x}^{\mathrm{2}} \left({x}^{\mathrm{2}}…