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AllQuestion and Answers: Page 1697

Question Number 38116 Answers: 0 Comments: 1

find I = ∫_0 ^∞ ((cos(λx))/(ch(2x)))dx

$${find}\:\:\:\:{I}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left(\lambda{x}\right)}{{ch}\left(\mathrm{2}{x}\right)}{dx}\: \\ $$

Question Number 38115 Answers: 0 Comments: 0

find ∫_0 ^∞ ((sin(2x))/(sh(3x)))dx

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{{sh}\left(\mathrm{3}{x}\right)}{dx}\: \\ $$

Question Number 38114 Answers: 0 Comments: 2

let I_n = ∫_0 ^(2π) (dx/((p +cost)^n )) with p>1 find the value of I_n

$${let}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\frac{{dx}}{\left({p}\:+{cost}\right)^{{n}} }\:\:{with}\:{p}>\mathrm{1} \\ $$$${find}\:{the}\:{value}\:{of}\:{I}_{{n}} \\ $$

Question Number 38113 Answers: 0 Comments: 2

let p>1 calculate ∫_0 ^(2π) (dt/((p +cost)^2 ))

$${let}\:{p}>\mathrm{1}\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\:\:\frac{{dt}}{\left({p}\:+{cost}\right)^{\mathrm{2}} } \\ $$

Question Number 38112 Answers: 1 Comments: 1

prove that arctan(x)= (i/2)ln(((i+x)/(i−x))) for ∣x∣<1

$${prove}\:{that}\:\:{arctan}\left({x}\right)=\:\frac{{i}}{\mathrm{2}}{ln}\left(\frac{{i}+{x}}{{i}−{x}}\right)\:{for}\:\mid{x}\mid<\mathrm{1} \\ $$

Question Number 38111 Answers: 1 Comments: 1

find lim_(x→0) ((e^x −[x])/x)

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{{e}^{{x}} \:−\left[{x}\right]}{{x}} \\ $$

Question Number 38110 Answers: 0 Comments: 0

let x from R find the value of f(x)= ∫_0 ^π ln(x^2 −2x cosθ +1)dθ

$${let}\:{x}\:{from}\:{R}\:{find}\:{the}\:{value}\:{of} \\ $$$${f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\pi} {ln}\left({x}^{\mathrm{2}} \:−\mathrm{2}{x}\:{cos}\theta\:+\mathrm{1}\right){d}\theta \\ $$

Question Number 38109 Answers: 0 Comments: 2

1) find S(x) = Σ_(n=1) ^∞ ((cos(nx))/n) 2) find Σ_(n=1) ^∞ (((−1)^n )/n)

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

Question Number 38108 Answers: 0 Comments: 1

find Σ_(n=1) ^∞ (((−1)^n )/n^2 )

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

Question Number 38107 Answers: 0 Comments: 0

find C = Σ_(n=1) ^∞ ((cos(nx))/n^2 )dx and S=Σ_(n=1) ^∞ ((sin(nx))/n^2 )

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

Question Number 38106 Answers: 0 Comments: 1

calculate ∫_0 ^(+∞) e^(−3t) ln(1+e^t )dt .

$${calculate}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:{e}^{−\mathrm{3}{t}} {ln}\left(\mathrm{1}+{e}^{{t}} \right){dt}\:. \\ $$

Question Number 38105 Answers: 1 Comments: 0

find ∫ (dx/((√(2x+1)) +(√(2x−1))))

$${find}\:\int\:\:\:\:\:\frac{{dx}}{\sqrt{\mathrm{2}{x}+\mathrm{1}}\:+\sqrt{\mathrm{2}{x}−\mathrm{1}}}\: \\ $$

Question Number 38104 Answers: 1 Comments: 0

find ∫_1 ^(+∞) (dx/((x^2 +2)(√(x+3))))

$${find}\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{2}\right)\sqrt{{x}+\mathrm{3}}} \\ $$

Question Number 38103 Answers: 0 Comments: 0

find I(λ)= ∫_0 ^(π/2) ((xdx)/(λ +tanx)) λ from R.

$${find}\:{I}\left(\lambda\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{xdx}}{\lambda\:+{tanx}}\:\:\lambda\:{from}\:{R}. \\ $$

Question Number 38102 Answers: 0 Comments: 0

let B_n = ∫_0 ^n e^(−(x−[x])^2 ) dx 1) calculate B_n 2) find lim_(n→+∞) B_n

$${let}\:{B}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:{e}^{−\left({x}−\left[{x}\right]\right)^{\mathrm{2}} } {dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{B}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{B}_{{n}} \\ $$

Question Number 38101 Answers: 0 Comments: 1

let A_n = ∫_0 ^n e^(x−[x]) dx 1) calculate A_n 2) find lim_(n→+∞) A_n

$${let}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:{e}^{{x}−\left[{x}\right]} {dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$

Question Number 38100 Answers: 0 Comments: 1

let A_n = ∫_0 ^n (x−[x])^2 dx 1) calculate A_n 2) find lim_(n→+∞) A_n

$${let}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \left({x}−\left[{x}\right]\right)^{\mathrm{2}} {dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$

Question Number 38099 Answers: 0 Comments: 5

x^x =0.25 find x

$${x}^{{x}} =\mathrm{0}.\mathrm{25} \\ $$$${find}\:{x} \\ $$

Question Number 38094 Answers: 1 Comments: 12

Question Number 38092 Answers: 0 Comments: 5

Question Number 38079 Answers: 1 Comments: 4

Question Number 38074 Answers: 1 Comments: 4

∫(dx/(a+btan^2 x)) = ?

$$\int\frac{{dx}}{{a}+{b}\mathrm{tan}\:^{\mathrm{2}} {x}}\:=\:? \\ $$

Question Number 38062 Answers: 0 Comments: 3

Question Number 38059 Answers: 1 Comments: 0

Prove that Σ(x_i −x^− )=0

$${Prove}\:{that}\:\Sigma\left({x}_{{i}} −\overset{−} {{x}}\right)=\mathrm{0} \\ $$

Question Number 38058 Answers: 3 Comments: 0

∫((tan x)/(a+btan^2 x)) dx = ?

$$\int\frac{\mathrm{tan}\:{x}}{{a}+{b}\mathrm{tan}\:^{\mathrm{2}} {x}}\:{dx}\:\:=\:? \\ $$

Question Number 38057 Answers: 1 Comments: 0

∫((cos 5x+cos 4x)/(1−2cos 3x))dx = ?

$$\int\frac{\mathrm{cos}\:\mathrm{5}{x}+\mathrm{cos}\:\mathrm{4}{x}}{\mathrm{1}−\mathrm{2cos}\:\mathrm{3}{x}}{dx}\:\:=\:? \\ $$

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