Question Number 53324 by 0955083339 last updated on 20/Jan/19 $$\mathrm{If}\:\mathrm{4}{a}\:+\:\mathrm{5}{b}\:+\:\mathrm{9}{c}=\mathrm{36}\:\mathrm{and}\:\mathrm{7}{a}\:+\:\mathrm{9}{b}\:+\:\mathrm{17}{c}=\mathrm{66}, \\ $$$$\mathrm{then}\:{a}+{b}+{c}=\_\_\_\_\_. \\ $$ Answered by Kunal12588 last updated on 21/Jan/19 $${let}\:{a}+{b}+{c}={k} \\ $$$$\mathrm{4}{a}+\mathrm{4}{b}+\mathrm{4}{c}+{b}+\mathrm{5}{c}=\mathrm{36} \\…
Question Number 53277 by 0955083339 last updated on 19/Jan/19 $$\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\:\frac{{x}}{\left(\mathrm{1}−{x}\right)^{\mathrm{3}/\mathrm{4}} }\:{dx}\:= \\ $$ Commented by maxmathsup by imad last updated on 19/Jan/19 $${let}\:{I}\:=\int_{\mathrm{0}}…
Question Number 53141 by gunawan last updated on 18/Jan/19 $$\mathrm{If}\:{n}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{unity},\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${a}−\:^{{n}} {C}_{\mathrm{1}} \left({a}−\mathrm{1}\right)+\:^{{n}} {C}_{\mathrm{2}} \left({a}−\mathrm{2}\right)−\:^{{n}} {C}_{\mathrm{3}} \left({a}−\mathrm{3}\right)+… \\ $$$$\:\:\:\:\:\:\:..+\left(−\mathrm{1}\right)^{{n}} \left({a}−{n}\right)\:\mathrm{is} \\ $$…
Question Number 52950 by gunawan last updated on 15/Jan/19 $$\:\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{3}+\mathrm{sin}\:\mathrm{2}{x}}\:{dx}\:= \\ $$ Commented by maxmathsup by imad last updated on 15/Jan/19 $${let}\:{A}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}}…
Question Number 52949 by gunawan last updated on 15/Jan/19 $$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{odd}\:\mathrm{function},\:\mathrm{then} \\ $$$$\underset{\:\mathrm{0}} {\overset{\pi} {\int}}\:{f}\:\left(\mathrm{cos}\:{x}\right)\:{dx}\:=\:\mathrm{2}\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:{f}\:\left(\mathrm{cos}\:{x}\right)\:{dx} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 15/Jan/19…
Question Number 52948 by gunawan last updated on 15/Jan/19 $$\mathrm{If}\:\:\:{f}\left({x}\right)\:=\underset{\:\mathrm{1}} {\overset{{x}} {\int}}\:\frac{\mathrm{log}\:{t}}{\mathrm{1}+{t}}\:{dt},\:\mathrm{then} \\ $$$$\:{f}\left({x}\right)+{f}\:\left(\frac{\mathrm{1}}{{x}}\:\right)=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{log}\:{x}\right)^{\mathrm{2}} \\ $$ Commented by maxmathsup by imad last updated on 15/Jan/19…
Question Number 52947 by gunawan last updated on 15/Jan/19 $$\underset{\:\mathrm{0}} {\overset{\pi} {\int}}\:\:\frac{{x}\:\mathrm{tan}\:{x}}{\mathrm{sec}\:{x}+\mathrm{cos}\:{x}}\:{dx}\:= \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 15/Jan/19 $$\int_{\mathrm{0}} ^{\pi} \frac{{x}×\frac{{sinx}}{{cosx}}}{\frac{\mathrm{1}}{{cosx}}+{cosx}}{dx} \\…
Question Number 52946 by gunawan last updated on 15/Jan/19 $$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\:\mathrm{log}\:\mathrm{sin}\:\mathrm{2}{x}\:{dx}\:= \\ $$ Commented by maxmathsup by imad last updated on 15/Jan/19 $${let}\:{A}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 52600 by Tip Top last updated on 10/Jan/19 $$\mathrm{If}\:{P}_{{n}} \:\mathrm{denotes}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{binomial}\: \\ $$$$\mathrm{coefficients}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+{x}\right)^{{n}} , \\ $$$$\mathrm{then}\:\frac{{P}_{{n}+\mathrm{1}} }{{P}_{{n}} }\:\mathrm{equals} \\ $$ Commented by Abdo msup.…
Question Number 51729 by shivshant0409 last updated on 30/Dec/18 $$\mathrm{81}^{\frac{\mathrm{1}}{\mathrm{4}}} ×\:\mathrm{9}^{\frac{\mathrm{3}}{\mathrm{2}}} ×\:\mathrm{27}^{\frac{\mathrm{4}}{\mathrm{3}}} =\:\_\_\_\_\_ \\ $$ Answered by aseerimad last updated on 30/Dec/18 $$\mathrm{81}^{\frac{\mathrm{1}}{\mathrm{4}}} ×\mathrm{9}^{\frac{\mathrm{3}}{\mathrm{2}}} ×\mathrm{27}^{\frac{\mathrm{4}}{\mathrm{3}}}…