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IntegrationQuestion and Answers: Page 243

Question Number 60311 Answers: 1 Comments: 2

∫(dx/(√(sec h^2 (x)+1))) dx

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

Question Number 60264 Answers: 0 Comments: 0

let f(t) =∫_0 ^∞ (e^(−3 [x^2 ]) /(x^2 +t^2 ))dx with t>0 1. determine a explicit form of f(t) 2. find also g(t) =∫_0 ^∞ (e^(−3[x^2 ]) /((x^2 +t^2 )^2 ))dx 3. find the values of integrals ∫_0 ^∞ (e^(−3[x^2 ]) /(x^2 +3))dx and ∫_0 ^∞ (e^(−3[x^2 ]) /((x^2 +4)^2 )) dx .

$${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−\mathrm{3}\:\left[{x}^{\mathrm{2}} \right]} }{{x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} }{dx}\:\:{with}\:{t}>\mathrm{0} \\ $$$$\mathrm{1}.\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({t}\right) \\ $$$$\mathrm{2}.\:{find}\:{also}\:{g}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−\mathrm{3}\left[{x}^{\mathrm{2}} \right]} }{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$$$\mathrm{3}.\:{find}\:{the}\:{values}\:{of}\:{integrals}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−\mathrm{3}\left[{x}^{\mathrm{2}} \right]} }{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx}\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−\mathrm{3}\left[{x}^{\mathrm{2}} \right]} }{\left({x}^{\mathrm{2}} \:+\mathrm{4}\right)^{\mathrm{2}} }\:{dx}\:. \\ $$

Question Number 60263 Answers: 0 Comments: 1

let U_n =∫_0 ^∞ (e^(−n[x^2 ]) /(x^2 +3)) dx 1) calculate U_n interms of n 2) find lim_(n→+∞) n U_n 3)determine nature of the serie Σ U_n

$${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−{n}\left[{x}^{\mathrm{2}} \right]} }{{x}^{\mathrm{2}} +\mathrm{3}}\:{dx}\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{n}\:{U}_{{n}} \\ $$$$\left.\mathrm{3}\right){determine}\:{nature}\:{of}\:{the}\:{serie}\:\:\Sigma\:{U}_{{n}} \\ $$

Question Number 60234 Answers: 1 Comments: 0

Question Number 60170 Answers: 0 Comments: 0

∫xsec^3 xdx

$$\int{x}\mathrm{sec}\:^{\mathrm{3}} {xdx} \\ $$

Question Number 60050 Answers: 1 Comments: 1

calculate ∫_0 ^1 (x^3 −2)(√(x^2 +3))dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \left({x}^{\mathrm{3}} −\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$

Question Number 60036 Answers: 1 Comments: 0

Question Number 60027 Answers: 1 Comments: 0

∫x^i dx=?

$$\int{x}^{{i}} {dx}=? \\ $$

Question Number 60025 Answers: 0 Comments: 0

Question Number 59999 Answers: 0 Comments: 0

let U_n =∫_0 ^∞ (e^(−n[x^2 ]) /((x^2 +3)^2 ))dx 1) find U_n interms of n 2) calvulate lim_(n→+∞) U_n 3)study the serie Σ U_n

$${let}\:{U}_{{n}} \:\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{n}\left[{x}^{\mathrm{2}} \right]} }{\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{calvulate}\:\:{lim}_{{n}\rightarrow+\infty} \:\:\:{U}_{{n}} \\ $$$$\left.\mathrm{3}\right){study}\:{the}\:{serie}\:\Sigma\:{U}_{{n}} \\ $$

Question Number 59998 Answers: 1 Comments: 3

find ∫ (dx/(acosx +bsinx)) with a and b reals

$${find}\:\int\:\frac{{dx}}{{acosx}\:+{bsinx}}\:\:{with}\:{a}\:{and}\:{b}\:{reals} \\ $$

Question Number 59991 Answers: 0 Comments: 2

Question Number 59990 Answers: 0 Comments: 0

Question Number 59960 Answers: 1 Comments: 0

Question Number 59946 Answers: 1 Comments: 1

Question Number 59926 Answers: 2 Comments: 1

Question Number 59906 Answers: 0 Comments: 0

∫(2x−1)dx

$$\int\left(\mathrm{2x}−\mathrm{1}\right)\mathrm{dx} \\ $$

Question Number 59905 Answers: 0 Comments: 1

∫(2x−1)^ 20

$$\int\left(\mathrm{2x}−\mathrm{1}\hat {\right)}\mathrm{20} \\ $$

Question Number 59904 Answers: 0 Comments: 0

(2x−1)^ 20

$$\left(\mathrm{2x}−\mathrm{1}\hat {\right)}\mathrm{20} \\ $$

Question Number 59902 Answers: 0 Comments: 1

∫sin (x)dx

$$\int\mathrm{sin}\:\left({x}\right){dx} \\ $$

Question Number 59901 Answers: 0 Comments: 0

∫sin (x)

$$\int\mathrm{sin}\:\left({x}\right) \\ $$

Question Number 59893 Answers: 0 Comments: 7

Question Number 59882 Answers: 0 Comments: 5

∫_0 ^∞ ((sin(x))/(x(x^2 +1))) dx

$$\int_{\mathrm{0}} ^{\infty} \frac{{sin}\left({x}\right)}{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}\:{dx} \\ $$

Question Number 59846 Answers: 0 Comments: 8

Question Number 59834 Answers: 1 Comments: 0

Question Number 59825 Answers: 0 Comments: 0

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