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Question Number 78314    Answers: 1   Comments: 1

resolve {_(logx_y =logy_x ) ^(x^y =y^x )

$${resolve} \\ $$$$\left\{_{{logx}_{{y}} ={logy}_{{x}} } ^{{x}^{{y}} ={y}^{{x}} } \right. \\ $$

Question Number 78311    Answers: 1   Comments: 2

Show that ((3+sin2x−2cos2x)/(1+3sin^2 x−cos2x ))=(2/5)(2+(1/(tanx)))

$$\mathrm{Show}\:\mathrm{that}\:\frac{\mathrm{3}+\mathrm{sin2}{x}−\mathrm{2cos2}{x}}{\mathrm{1}+\mathrm{3}{sin}^{\mathrm{2}} {x}−{cos}\mathrm{2}{x}\:}=\frac{\mathrm{2}}{\mathrm{5}}\left(\mathrm{2}+\frac{\mathrm{1}}{{tanx}}\right) \\ $$

Question Number 78307    Answers: 0   Comments: 0

Question Number 78306    Answers: 1   Comments: 0

The sum of age of Hamadou his wife and theirs son is 100. n years ago the wife had the quadruple of his son′s age and Hamadou was 6 time older than his son. Determine theirs ages. i want that you help me to found equations. i found the first : x+y+z=100 please help me for the rest.

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{age}\:\mathrm{of}\:\mathrm{Hamadou}\:\:\: \\ $$$$\mathrm{his}\:\mathrm{wife}\:\mathrm{and}\:\mathrm{theirs}\:\mathrm{son}\:\mathrm{is}\:\mathrm{100}. \\ $$$$\mathrm{n}\:\mathrm{years}\:\mathrm{ago}\:\mathrm{the}\:\mathrm{wife}\:\mathrm{had}\:\mathrm{the}\: \\ $$$$\mathrm{quadruple}\:\mathrm{of}\:\mathrm{his}\:\mathrm{son}'\mathrm{s}\:\mathrm{age}\:\mathrm{and}\: \\ $$$$\mathrm{Hamadou}\:\mathrm{was}\:\mathrm{6}\:\mathrm{time}\:\mathrm{older}\:\mathrm{than} \\ $$$$\mathrm{his}\:\mathrm{son}. \\ $$$$\mathrm{Determine}\:\mathrm{theirs}\:\mathrm{ages}. \\ $$$$ \\ $$$$\mathrm{i}\:\mathrm{want}\:\mathrm{that}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{found} \\ $$$$\mathrm{equations}. \\ $$$$\mathrm{i}\:\mathrm{found}\:\mathrm{the}\:\mathrm{first}\::\:{x}+{y}+{z}=\mathrm{100} \\ $$$${please}\:{help}\:{me}\:{for}\:{the}\:{rest}. \\ $$

Question Number 78305    Answers: 0   Comments: 0

∫^∞^ 5646778727711=778888877−{116567×622−[66262−712]66666}

$$\overset{\hat {\infty}} {\int}\mathrm{5646778727711}=\mathrm{778888877}−\left\{\mathrm{116567}×\mathrm{622}−\left[\mathrm{66262}−\mathrm{712}\right]\mathrm{66666}\right\} \\ $$$$ \\ $$$$ \\ $$

Question Number 78309    Answers: 1   Comments: 0

Question Number 78289    Answers: 1   Comments: 1

Question Number 78286    Answers: 0   Comments: 1

find A_n =∫∫_([0,n[) e^(−(x^2 +3y^2 )) sin(x^2 +3y^2 )dxdy and lim_(n→+∞) A_n find nature of the serie Σn A_n

$${find}\:{A}_{{n}} =\int\int_{\left[\mathrm{0},{n}\left[\right.\right.} \:\:{e}^{−\left({x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} \right)} {sin}\left({x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} \right){dxdy} \\ $$$${and}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$$${find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma{n}\:{A}_{{n}} \\ $$

Question Number 78284    Answers: 0   Comments: 1

calculate ∫∫_D xy(√(x^2 +2y^2 ))dxdy D={(x,y)/0≤x≤1 and 0≤y≤(√(1−x^2 ))}

$${calculate}\:\int\int_{{D}} {xy}\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} }{dxdy} \\ $$$${D}=\left\{\left({x},{y}\right)/\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\:\mathrm{0}\leqslant{y}\leqslant\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right\} \\ $$

Question Number 78283    Answers: 0   Comments: 3

calculate ∫∫_D (x^2 +2y)dxdy with D={(x,y)∈R^2 / x^2 ≥y and y≥x^2 }

$${calculate}\:\int\int_{{D}} \:\left({x}^{\mathrm{2}} +\mathrm{2}{y}\right){dxdy} \\ $$$${with}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:{x}^{\mathrm{2}} \geqslant{y}\:{and}\:{y}\geqslant{x}^{\mathrm{2}} \right\} \\ $$

Question Number 78281    Answers: 0   Comments: 0

calculate ∫∫_W ((x^2 −3y^2 )/e^(x^2 +y^2 ) )dxdy with W =[0,1]×[0,1]

$${calculate}\:\:\int\int_{{W}} \:\frac{{x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} }{{e}^{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } }{dxdy} \\ $$$${with}\:{W}\:=\left[\mathrm{0},\mathrm{1}\right]×\left[\mathrm{0},\mathrm{1}\right] \\ $$

Question Number 78280    Answers: 0   Comments: 0

find by recurrence J_(n,p) =∫_0 ^1 x^n (arctanx)^p dx stydy the serie Σ_(n≥0 and p≥0) J_(n,p)

$${find}\:{by}\:{recurrence} \\ $$$${J}_{{n},{p}} \:=\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} \left({arctanx}\right)^{{p}} {dx} \\ $$$${stydy}\:{the}\:{serie}\:\sum_{{n}\geqslant\mathrm{0}\:{and}\:{p}\geqslant\mathrm{0}} \:\:{J}_{{n},{p}} \\ $$

Question Number 78277    Answers: 0   Comments: 0

calculate ∫∫_W (e^(−x^2 −y^2 ) /(2(√(x^2 +y^2 ))+3))dxdy with W ={ (x,y)/ x>0 and y>0}

$${calculate}\:\int\int_{{W}} \:\:\:\frac{{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } }{\mathrm{2}\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }+\mathrm{3}}{dxdy} \\ $$$${with}\:{W}\:=\left\{\:\left({x},{y}\right)/\:{x}>\mathrm{0}\:{and}\:{y}>\mathrm{0}\right\} \\ $$

Question Number 78276    Answers: 0   Comments: 1

find I_n =∫∫_([1,n]^2 ) (√(x^2 +y^2 ))ln(x^2 +y^2 )dxdy

$${find}\:{I}_{{n}} =\int\int_{\left[\mathrm{1},{n}\right]^{\mathrm{2}} } \:\:\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{ln}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dxdy} \\ $$

Question Number 78273    Answers: 0   Comments: 1

let f(θ) =∫_0 ^(π/4) (dx/(1+sinθ sinx)) with 0<θ<(π/2) 1) explicite f(θ) 2) calculate ∫_0 ^(π/4) (dx/((1+sinθ sinx)^2 ))

$${let}\:{f}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{dx}}{\mathrm{1}+{sin}\theta\:{sinx}} \\ $$$$ \\ $$$${with}\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$$$\left.\mathrm{1}\right)\:{explicite}\:{f}\left(\theta\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{dx}}{\left(\mathrm{1}+{sin}\theta\:{sinx}\right)^{\mathrm{2}} } \\ $$

Question Number 78271    Answers: 0   Comments: 1

calculate A_θ =∫_0 ^(π/2) (dx/(2+cosθ sinx)) −π<θ<π

$${calculate}\:{A}_{\theta} \:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\mathrm{2}+{cos}\theta\:{sinx}} \\ $$$$−\pi<\theta<\pi \\ $$

Question Number 78270    Answers: 1   Comments: 1

find ∫_0 ^1 ((ln(1−x^2 )ln(x))/x^2 )dx prove first the convergence.

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right){ln}\left({x}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$$${prove}\:{first}\:{the}\:{convergence}. \\ $$

Question Number 78269    Answers: 1   Comments: 1

let f(a) =∫_0 ^∞ ((cos(ax))/(x^2 +a^2 ))dx with a>0 find ∫_1 ^2 f(a)da

$${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({ax}\right)}{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dx}\:{with} \\ $$$${a}>\mathrm{0}\:\:{find}\:\:\:\int_{\mathrm{1}} ^{\mathrm{2}} {f}\left({a}\right){da} \\ $$

Question Number 78267    Answers: 0   Comments: 1

find ∫_(−∞) ^(+∞) ((x^2 −x)/(x^4 −x^2 +3))dx

$${find}\:\:\int_{−\infty} ^{+\infty} \:\frac{{x}^{\mathrm{2}} −{x}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$

Question Number 78266    Answers: 1   Comments: 2

calculate f(a)=∫_0 ^1 ln(1−ax^3 )dx with 0<a<1

$${calculate}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{ax}^{\mathrm{3}} \right){dx} \\ $$$${with}\:\mathrm{0}<{a}<\mathrm{1} \\ $$

Question Number 78264    Answers: 0   Comments: 4

let I =∫_0 ^π x cos^4 x dxand J=∫_0 ^π x sin^4 xdx 1) calculate I+J and I−J 2) find the values of I and J

$${let}\:{I}\:=\int_{\mathrm{0}} ^{\pi} {x}\:{cos}^{\mathrm{4}} {x}\:{dxand}\:{J}=\int_{\mathrm{0}} ^{\pi} {x}\:{sin}^{\mathrm{4}} {xdx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}+{J}\:{and}\:{I}−{J} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:{I}\:{and}\:{J} \\ $$

Question Number 78263    Answers: 1   Comments: 2

find lim_(n→+∞) Σ_(k=1) ^n sin((1/(k+n)))

$${find}\:{lim}_{{n}\rightarrow+\infty} \sum_{{k}=\mathrm{1}} ^{{n}} {sin}\left(\frac{\mathrm{1}}{{k}+{n}}\right) \\ $$

Question Number 78265    Answers: 1   Comments: 0

find ∫ ((sin^3 x)/(tan^5 x))dx

$${find}\:\int\:\:\frac{{sin}^{\mathrm{3}} {x}}{{tan}^{\mathrm{5}} {x}}{dx} \\ $$

Question Number 78256    Answers: 0   Comments: 0

Evaluate Σa_1 a_2 a_3 as a function of a_i

$$\mathrm{Evaluate}\:\Sigma\mathrm{a}_{\mathrm{1}} \mathrm{a}_{\mathrm{2}} \mathrm{a}_{\mathrm{3}} \: \\ $$$$\mathrm{as}\:\mathrm{a}\:\mathrm{function}\:\mathrm{of}\:\:\mathrm{a}_{\mathrm{i}} \: \\ $$$$ \\ $$$$ \\ $$

Question Number 78261    Answers: 0   Comments: 3

let U_n =∫_0 ^1 (x^n /(1+x))dx calculate U_n +U_(n+1)

$${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{x}^{{n}} }{\mathrm{1}+{x}}{dx}\:\:{calculate} \\ $$$${U}_{{n}} \:+{U}_{{n}+\mathrm{1}} \\ $$

Question Number 78251    Answers: 1   Comments: 0

∫((x+4)/(x−(x)^(1/3) )) dx

$$\int\frac{{x}+\mathrm{4}}{{x}−\sqrt[{\mathrm{3}}]{{x}}}\:{dx}\: \\ $$

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