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Question Number 68043 Answers: 1 Comments: 1

∫_(π/2) ^π e^(cosx) (√(1−e^(cosx) )) sinx dx

$$\int_{\pi/\mathrm{2}} ^{\pi} {e}^{{cosx}} \sqrt{\mathrm{1}−{e}^{{cosx}} }\:{sinx}\:{dx} \\ $$

Question Number 68728 Answers: 0 Comments: 0

dear scientist. i did some research on the energy obtained from the sun any other source by a liquid, of density ρ , velocity v, viscosity η and distance travelled d. i came out with the equation E = k ( vρ η^3 d^2 ) where k is a costant i still need to determine from more experiment. But please i want you guys great people to check if the equation is in confirmity and if atall it is correct so i can do some changes. thanks in advanced dear scientist.

$${dear}\:{scientist}. \\ $$$${i}\:{did}\:{some}\:{research}\:{on}\:{the}\:{energy}\:{obtained}\:{from}\:{the}\:{sun} \\ $$$${any}\:{other}\:{source}\:\:{by}\:{a}\:{liquid},\:{of}\:{density}\:\rho\:,\:{velocity}\:\:{v},\:\:{viscosity}\:\eta\:{and}\:{distance}\: \\ $$$${travelled}\:\:\:{d}. \\ $$$$ \\ $$$${i}\:{came}\:{out}\:{with}\:{the}\:{equation}\: \\ $$$$\:\:\:{E}\:=\:{k}\:\left(\:{v}\rho\:\eta^{\mathrm{3}} \:{d}^{\mathrm{2}} \right) \\ $$$${where}\:\:{k}\:{is}\:{a}\:{costant}\:{i}\:{still}\:{need}\:{to}\:{determine}\:{from}\:{more} \\ $$$${experiment}.\:{But}\:{please}\:{i}\:{want}\:{you}\:{guys}\:\:{great}\:{people}\:{to}\: \\ $$$${check}\:{if}\:{the}\:{equation}\:{is}\:{in}\:{confirmity}\:{and}\:{if}\:{atall}\:{it}\:{is}\:{correct} \\ $$$${so}\:{i}\:{can}\:{do}\:{some}\:{changes}. \\ $$$$ \\ $$$${thanks}\:{in}\:{advanced}\:\:{dear}\:{scientist}. \\ $$$$ \\ $$

Question Number 67413 Answers: 0 Comments: 0

Question Number 67398 Answers: 0 Comments: 2

solve the defrintion eguation (xp^2 −p+2x)=0 when p=dy/dx

$${solve}\:{the}\:{defrintion}\:{eguation}\:\left({xp}^{\mathrm{2}} −{p}+\mathrm{2}{x}\right)=\mathrm{0} \\ $$$${when}\:{p}={dy}/{dx} \\ $$

Question Number 67396 Answers: 0 Comments: 2

Question Number 67393 Answers: 0 Comments: 1

let y=(x−3)φ(2x+1) find dy/dx when x=2

$${let}\:{y}=\left({x}−\mathrm{3}\right)\phi\left(\mathrm{2}{x}+\mathrm{1}\right) \\ $$$${find}\:{dy}/{dx}\:{when}\:{x}=\mathrm{2} \\ $$

Question Number 67392 Answers: 0 Comments: 0

∫(6x

$$\int\left(\mathrm{6}{x}\right. \\ $$

Question Number 67386 Answers: 2 Comments: 8

Question Number 67385 Answers: 0 Comments: 0

find ∫ x((√((1−x^2 )/(1+x^2 ))))dx

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

Question Number 67384 Answers: 0 Comments: 1

find Σ_(n=1) ^∞ ((cos(nx))/n^2 )

$${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{cos}\left({nx}\right)}{{n}^{\mathrm{2}} } \\ $$

Question Number 67382 Answers: 0 Comments: 3

calculate if there are maxims and minimus of the following function: y= { ((x^2 +1 if x⪇1)),((−x+4 if x≥1)) :}

$${calculate}\:{if}\:{there}\:{are}\:{maxims}\:{and}\:{minimus}\:{of} \\ $$$${the}\:{following}\:{function}: \\ $$$${y}=\begin{cases}{{x}^{\mathrm{2}} +\mathrm{1}\:{if}\:{x}\lneq\mathrm{1}}\\{−{x}+\mathrm{4}\:{if}\:{x}\geqslant\mathrm{1}}\end{cases} \\ $$

Question Number 67381 Answers: 0 Comments: 1

let f(x) =x^2 2π periodic even develop f at fourier serie

$${let}\:{f}\left({x}\right)\:={x}^{\mathrm{2}} \:\:\:\:\:\:\:\mathrm{2}\pi\:{periodic}\:\:{even}\:\:{develop}\:{f}\:{at}\:{fourier}\:{serie} \\ $$

Question Number 67380 Answers: 0 Comments: 1

solve the (d.e.) ( x^2 −x+1 )y^′ −(2x+3)y =x^2 e^x

$${solve}\:{the}\:\left({d}.{e}.\right)\:\:\:\:\left(\:{x}^{\mathrm{2}} −{x}+\mathrm{1}\:\:\:\:\:\:\right){y}^{'} −\left(\mathrm{2}{x}+\mathrm{3}\right){y}\:={x}^{\mathrm{2}} \:{e}^{{x}} \\ $$

Question Number 67379 Answers: 0 Comments: 2

let f(x) =e^(−∣x∣) 2π periodic even developp f at fourier serie

$${let}\:\:{f}\left({x}\right)\:={e}^{−\mid{x}\mid} \:\:\:\:\:\:\mathrm{2}\pi\:\:{periodic}\:{even} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$

Question Number 67378 Answers: 0 Comments: 1

let f(x) =x^3 ,2π periodic odd developp f at fourier serie

$${let}\:{f}\left({x}\right)\:={x}^{\mathrm{3}} \:\:\:\:\:\:,\mathrm{2}\pi\:{periodic}\:{odd} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}\: \\ $$

Question Number 67374 Answers: 0 Comments: 3

find ∫ (1+(1/x^2 ))arctan(1−(1/x))dx

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

Question Number 67371 Answers: 1 Comments: 0

Question Number 67373 Answers: 1 Comments: 4

simplify S_n (x) =Σ_(k=0) ^n C_n ^k cos^4 (πkx) 2) calculate I_n =∫_0 ^(1/3) S_n (x)dx

$${simplify}\:\:\:{S}_{{n}} \left({x}\right)\:=\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{cos}^{\mathrm{4}} \left(\pi{kx}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{3}}} \:{S}_{{n}} \left({x}\right){dx} \\ $$

Question Number 67359 Answers: 1 Comments: 1

∫siny/y dy

$$\int{siny}/{y}\:\:{dy} \\ $$

Question Number 67350 Answers: 1 Comments: 1

Question Number 67349 Answers: 1 Comments: 0

Solve for y(x) xy′ = y + 2x^3 sin^2 ((y/x))

$$\mathrm{Solve}\:\mathrm{for}\:{y}\left({x}\right) \\ $$$${xy}'\:=\:{y}\:+\:\mathrm{2}{x}^{\mathrm{3}} \mathrm{sin}^{\mathrm{2}} \left(\frac{{y}}{{x}}\right) \\ $$

Question Number 67345 Answers: 1 Comments: 0

3sinx+5cosx=5 then prove that 5sinx−3cox= +3

$$\mathrm{3}{sinx}+\mathrm{5}{cosx}=\mathrm{5}\:{then}\:{prove}\:{that}\: \\ $$$$\mathrm{5}{sinx}−\mathrm{3}{cox}=\:+\mathrm{3} \\ $$

Question Number 67342 Answers: 0 Comments: 1

find the value of ∫_(−∞) ^∞ ((sin(2x^2 ))/((x^2 −x +3)^3 ))dx

$${find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{\infty} \:\:\:\frac{{sin}\left(\mathrm{2}{x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} −{x}\:+\mathrm{3}\right)^{\mathrm{3}} }{dx} \\ $$

Question Number 67310 Answers: 1 Comments: 2

calculate ∫_(−∞) ^(+∞) (dx/(x^4 +x^2 +1))

$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} \:+\mathrm{1}} \\ $$

Question Number 67307 Answers: 1 Comments: 1

Question Number 67299 Answers: 2 Comments: 5

G(x)= (x+1)(x+3)Q(x) + px +q a) Given that G(x) leaves a remainder of 8 and −24 when divided by (x+1) and (x+3) respectively,find the remainder when G(x) is divided by (x+1)(x+3). b) Given that x+2 is a factor of G(x) and that the graph of G(x) passes through the point with coordinates (0,6) find G(x)

$${G}\left({x}\right)=\:\left({x}+\mathrm{1}\right)\left({x}+\mathrm{3}\right){Q}\left({x}\right)\:+\:{px}\:+{q} \\ $$$$\left.{a}\right)\:{Given}\:{that}\:{G}\left({x}\right)\:{leaves}\:{a}\:{remainder}\:{of}\:\mathrm{8}\:{and}\:−\mathrm{24}\:{when}\:{divided}\:{by}\:\left({x}+\mathrm{1}\right)\:{and}\: \\ $$$$\left({x}+\mathrm{3}\right)\:{respectively},{find}\:{the}\:{remainder}\:{when}\:{G}\left({x}\right)\:{is}\:{divided}\:{by}\:\left({x}+\mathrm{1}\right)\left({x}+\mathrm{3}\right). \\ $$$$\left.{b}\right)\:\:{Given}\:{that}\:{x}+\mathrm{2}\:{is}\:{a}\:{factor}\:{of}\:{G}\left({x}\right)\:{and}\:{that}\:{the}\:{graph}\:{of}\:{G}\left({x}\right)\:{passes}\:{through} \\ $$$${the}\:{point}\:{with}\:{coordinates}\:\left(\mathrm{0},\mathrm{6}\right)\:{find}\:{G}\left({x}\right) \\ $$

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