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Question Number 45164    Answers: 0   Comments: 6

Question Number 45163    Answers: 0   Comments: 0

Evaluate ∫_0 ^∞ ∫_0 ^t e^(−t) ((sinu)/u)du dt

$$\mathrm{Evaluate}\:\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\mathrm{t}} \mathrm{e}^{−\mathrm{t}} \frac{\mathrm{sinu}}{\mathrm{u}}\mathrm{du}\:\mathrm{dt} \\ $$

Question Number 45162    Answers: 0   Comments: 0

L{(t^2 +3t+2)H(t−1)+((sin 2t)/t)δ(t−(π/4))}

$$\mathrm{L}\left\{\left(\mathrm{t}^{\mathrm{2}} +\mathrm{3t}+\mathrm{2}\right)\mathrm{H}\left(\mathrm{t}−\mathrm{1}\right)+\frac{\mathrm{sin}\:\mathrm{2t}}{\mathrm{t}}\delta\left(\mathrm{t}−\frac{\pi}{\mathrm{4}}\right)\right\} \\ $$

Question Number 45160    Answers: 0   Comments: 0

L{(√(1+sin t))+∫_0 ^t cosht cost dt}

$$\mathrm{L}\left\{\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{t}}+\int_{\mathrm{0}} ^{\mathrm{t}} \mathrm{cosht}\:\mathrm{cost}\:\mathrm{dt}\right\} \\ $$

Question Number 45158    Answers: 0   Comments: 1

∫((e^(2x) −e^x +1)/((e^x sinx+cosx)(e^x cosx−sinx)))dx =?

$$\:\:\int\frac{{e}^{\mathrm{2}{x}} −{e}^{{x}} +\mathrm{1}}{\left({e}^{{x}} {sinx}+{cosx}\right)\left({e}^{{x}} {cosx}−{sinx}\right)}{dx}\:=? \\ $$

Question Number 45129    Answers: 1   Comments: 1

Question Number 45128    Answers: 1   Comments: 1

Question Number 45122    Answers: 0   Comments: 1

Question Number 45117    Answers: 1   Comments: 3

Prove that ∫_0 ^1 ((x^a −1)/(log x)) dx = log (a+1).

$${Prove}\:{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{x}^{{a}} −\mathrm{1}}{\mathrm{log}\:{x}}\:{dx}\:=\:\mathrm{log}\:\left({a}+\mathrm{1}\right). \\ $$

Question Number 45112    Answers: 0   Comments: 3

Question Number 45125    Answers: 1   Comments: 0

Question Number 45127    Answers: 1   Comments: 0

Question Number 45126    Answers: 0   Comments: 1

Question Number 45085    Answers: 1   Comments: 0

A motorist travelled from A to B. This is a distance of 142km at an average speed of 60kmhr^(−1) .He spent 5/2hours in B and then returned to A at an average speed of 80kmh^(−1) . a)At what time did the man arrive back at A b)find the average speed for the_ total journey.

$${A}\:{motorist}\:{travelled}\:{from}\:{A}\:{to}\:{B}. \\ $$$${This}\:{is}\:{a}\:{distance}\:{of}\:\mathrm{142}{km}\:{at}\:{an} \\ $$$${average}\:{speed}\:{of}\:\mathrm{60}{kmhr}^{−\mathrm{1}} .{He} \\ $$$${spent}\:\mathrm{5}/\mathrm{2}{hours}\:{in}\:{B}\:{and}\:{then} \\ $$$${returned}\:{to}\:{A}\:{at}\:{an}\:{average}\:{speed} \\ $$$${of}\:\mathrm{80}{kmh}^{−\mathrm{1}} . \\ $$$$\left.{a}\right){At}\:{what}\:{time}\:{did}\:{the}\:{man}\:{arrive} \\ $$$${back}\:{at}\:{A} \\ $$$$\left.{b}\right){find}\:{the}\:{average}\:{speed}\:{for}\:{the}_{} \\ $$$${total}\:{journey}. \\ $$

Question Number 45789    Answers: 2   Comments: 0

(18+5x)×3=309

$$ \\ $$$$\left(\mathrm{18}+\mathrm{5x}\right)×\mathrm{3}=\mathrm{309} \\ $$

Question Number 45082    Answers: 1   Comments: 1

Question Number 45080    Answers: 0   Comments: 1

find Σ_(n=0) ^∞ (1/((2n+1)^4 ))

$${find}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{4}} } \\ $$

Question Number 45075    Answers: 1   Comments: 2

∫_0 ^∞ (t^(a−1) /(1+t))dt=(π/(sin(πa))) please prove that

$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{t}^{\mathrm{a}−\mathrm{1}} }{\mathrm{1}+\mathrm{t}}\mathrm{dt}=\frac{\pi}{\mathrm{sin}\left(\pi\mathrm{a}\right)}\:\:\: \\ $$$$\mathrm{please}\:\mathrm{prove}\:\mathrm{that} \\ $$

Question Number 45067    Answers: 1   Comments: 2

Question Number 45063    Answers: 0   Comments: 2

∫_0 ^(2π) e^(cos θ) cos (sin θ)dθ = ?

$$\int_{\mathrm{0}} ^{\mathrm{2}\pi} {e}^{\mathrm{cos}\:\theta} \mathrm{cos}\:\left(\mathrm{sin}\:\theta\right){d}\theta\:=\:? \\ $$

Question Number 45045    Answers: 1   Comments: 0

find the value of ∫_0 ^∞ (t^3 /(1+e^t ))dt .

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{t}^{\mathrm{3}} }{\mathrm{1}+{e}^{{t}} }{dt}\:. \\ $$

Question Number 45044    Answers: 0   Comments: 1

let f(x) =x^2 , function 2π peridic even 1) developp f at fourier serie 2)find the value of Σ_(n=1) ^∞ (1/n^4 )

$${let}\:{f}\left({x}\right)\:={x}^{\mathrm{2}} \:,\:{function}\:\mathrm{2}\pi\:{peridic}\:{even} \\ $$$$\left.\mathrm{1}\right)\:{developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{4}} } \\ $$

Question Number 45043    Answers: 3   Comments: 0

let f(x)=((1+(√(1+x^2 )))/x) 1) calculate ∫_1 ^3 f(x)dx 2) determine f^(−1) (x) 3) find ∫ f^(−1) (x)dx .

$${let}\:{f}\left({x}\right)=\frac{\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{{x}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{3}} {f}\left({x}\right){dx} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{f}^{−\mathrm{1}} \left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:\int\:{f}^{−\mathrm{1}} \left({x}\right){dx}\:\:. \\ $$

Question Number 45038    Answers: 0   Comments: 4

Question Number 45029    Answers: 0   Comments: 0

x^2 =12y

$$\mathrm{x}^{\mathrm{2}} =\mathrm{12y} \\ $$

Question Number 45021    Answers: 2   Comments: 0

∫_0 ^(π/2) (dx/(1+tan^(13) x)) = ?

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{dx}}{\mathrm{1}+\mathrm{tan}\:^{\mathrm{13}} {x}}\:=\:? \\ $$

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