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Question Number 37110    Answers: 1   Comments: 2

prove that (cosπ›βˆ’sin𝛝)^2 +(cosec𝛝+sin𝛝)^2 =2

$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\left(\boldsymbol{\mathrm{cos}\vartheta}βˆ’\boldsymbol{\mathrm{sin}\vartheta}\right)^{\mathrm{2}} +\left(\boldsymbol{\mathrm{cosec}\vartheta}+\boldsymbol{\mathrm{sin}\vartheta}\right)^{\mathrm{2}} =\mathrm{2} \\ $$

Question Number 37108    Answers: 1   Comments: 0

If 4x+8cos x+tan xβˆ’2sec xβˆ’4log {cosx(1+sin x)}β‰₯6 βˆ€ x Ξ΅ [0,ψ) then largest value of ψ is ?

$$\mathrm{If}\:\mathrm{4}{x}+\mathrm{8cos}\:{x}+\mathrm{tan}\:{x}βˆ’\mathrm{2sec}\:{x}βˆ’\mathrm{4log}\:\left\{\mathrm{cos}{x}\left(\mathrm{1}+\mathrm{sin}\:{x}\right)\right\}\geqslant\mathrm{6} \\ $$$$\forall\:{x}\:\epsilon\:\left[\mathrm{0},\psi\right)\:\mathrm{then}\:\mathrm{largest}\:\mathrm{value}\:\mathrm{of}\:\psi\:\mathrm{is}\:? \\ $$

Question Number 37089    Answers: 1   Comments: 10

Question Number 37084    Answers: 0   Comments: 2

solve using matrix method x βˆ’ y= 4 2x βˆ’ 3y= 5

$$\:\:{solve}\:{using}\:{matrix}\:{method} \\ $$$$\:\:\:\:\:\:{x}\:βˆ’\:{y}=\:\mathrm{4} \\ $$$$\:\:\:\:\:\mathrm{2}{x}\:βˆ’\:\mathrm{3}{y}=\:\mathrm{5} \\ $$

Question Number 37081    Answers: 0   Comments: 1

Question Number 37079    Answers: 1   Comments: 0

Question Number 37073    Answers: 2   Comments: 2

Question Number 37071    Answers: 2   Comments: 1

find the value of ∫_0 ^(Ο€/2) ((xdx)/(1+cosx))

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{xdx}}{\mathrm{1}+{cosx}} \\ $$

Question Number 37067    Answers: 2   Comments: 1

find ∫ (dx/((x+1)(√(1+x^2 ))))

$${find}\:\int\:\:\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \\ $$

Question Number 37059    Answers: 0   Comments: 0

Question Number 37058    Answers: 1   Comments: 0

Question Number 37048    Answers: 0   Comments: 2

to everybody: if you solved an integral, please test your solution by differentiating. Iβ€²m doing the same. thank you so much! MJS

$$\mathrm{to}\:\mathrm{everybody}: \\ $$$$\mathrm{if}\:\mathrm{you}\:\mathrm{solved}\:\mathrm{an}\:\mathrm{integral},\:\mathrm{please}\:\mathrm{test}\:\mathrm{your} \\ $$$$\mathrm{solution}\:\mathrm{by}\:\mathrm{differentiating}.\:\mathrm{I}'\mathrm{m}\:\mathrm{doing}\:\mathrm{the} \\ $$$$\mathrm{same}.\:\mathrm{thank}\:\mathrm{you}\:\mathrm{so}\:\mathrm{much}! \\ $$$${MJS} \\ $$

Question Number 37045    Answers: 1   Comments: 1

Question Number 37037    Answers: 4   Comments: 0

If ((a+bβˆ’c)/(a+b)) = ((b+cβˆ’a)/(b+c)) =((c+aβˆ’b)/(c+a)) and a+b+c β‰  0 then which of the following is true 1) a=βˆ’b=c 2)βˆ’a=βˆ’b=c 3) a=b=c 4) a=bβ‰ c

$${If}\:\frac{{a}+{b}βˆ’{c}}{{a}+{b}}\:=\:\frac{{b}+{c}βˆ’{a}}{{b}+{c}}\:=\frac{{c}+{a}βˆ’{b}}{{c}+{a}}\:{and}\: \\ $$$$\mathrm{a}+\mathrm{b}+\mathrm{c}\:\neq\:\mathrm{0}\:{then}\:{which}\:{of}\:{the}\:{following} \\ $$$$\left.{i}\left.{s}\:{true}\:\mathrm{1}\right)\:{a}=βˆ’{b}={c}\:\mathrm{2}\right)βˆ’{a}=βˆ’{b}={c}\: \\ $$$$\left.\mathrm{3}\left.\right)\:\mathrm{a}=\mathrm{b}=\mathrm{c}\:\mathrm{4}\right)\:\mathrm{a}=\mathrm{b}\neq{c} \\ $$

Question Number 37036    Answers: 0   Comments: 3

∫_0 ^( a) (1βˆ’((bβˆ’x)/(√((bβˆ’x)^2 +cx)))) dx = ?

$$\int_{\mathrm{0}} ^{\:\:{a}} \left(\mathrm{1}βˆ’\frac{{b}βˆ’{x}}{\sqrt{\left({b}βˆ’{x}\right)^{\mathrm{2}} +{cx}}}\right)\:{dx}\:=\:? \\ $$

Question Number 37032    Answers: 1   Comments: 1

Question Number 37028    Answers: 1   Comments: 0

∫((2xβˆ’1)/(5x^2 βˆ’x+2)) dx = ?

$$\int\frac{\mathrm{2}{x}βˆ’\mathrm{1}}{\mathrm{5}{x}^{\mathrm{2}} βˆ’{x}+\mathrm{2}}\:{dx}\:\:=\:\:? \\ $$

Question Number 37026    Answers: 0   Comments: 0

Question Number 37023    Answers: 0   Comments: 0

Question Number 37022    Answers: 0   Comments: 0

Question Number 37021    Answers: 0   Comments: 0

Question Number 37020    Answers: 0   Comments: 0

Question Number 37018    Answers: 3   Comments: 3

Question Number 37010    Answers: 0   Comments: 0

Question Number 37009    Answers: 0   Comments: 0

Question Number 37008    Answers: 0   Comments: 0

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