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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)) = ?

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

Question Number 45020 Answers: 2 Comments: 5

Question Number 45019 Answers: 1 Comments: 0

Question Number 45014 Answers: 1 Comments: 6

6÷2(1+2)? which ans is correct between 1or 9 why do i look at the mobile phone calculator is 9 and when i check to scientific calculator the ans is 1.i want to clarify correctly where you are.

Question Number 44994 Answers: 1 Comments: 0

∫e^x (((1+sin x)/(1−cos x)))dx = ?

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

Question Number 44993 Answers: 1 Comments: 1

∫(x/(sin x))dx=?

$$\int\frac{\mathrm{x}}{\mathrm{sin}\:\mathrm{x}}\mathrm{dx}=? \\ $$

Question Number 44992 Answers: 2 Comments: 0

∫e^x (((1−sin x)/(1+cos x)))dx ?

$$\int\mathrm{e}^{\mathrm{x}} \left(\frac{\mathrm{1}−\mathrm{sin}\:\mathrm{x}}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}\right)\mathrm{dx}\:? \\ $$

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