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IntegrationQuestion and Answers: Page 244

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

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

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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

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

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Question Number 59800 Answers: 2 Comments: 0

find the general solution y(t) of the ordinary differential equation y′′ + ω^2 y=cos ωt ,where w>0

$${find}\:{the}\:{general}\:{solution}\:{y}\left({t}\right)\:{of}\:{the} \\ $$$${ordinary}\:{differential}\:{equation} \\ $$$${y}''\:+\:\omega^{\mathrm{2}} {y}=\mathrm{cos}\:\omega{t}\:,{where}\:{w}>\mathrm{0} \\ $$

Question Number 59807 Answers: 1 Comments: 0

∫((x−1)/(√(2x−x^2 ))) dx

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

Question Number 59732 Answers: 2 Comments: 0

find I_n =∫ (dx/(sin^n x)) with n integr natural.

$${find}\:{I}_{{n}} =\int\:\:\frac{{dx}}{{sin}^{{n}} {x}}\:\:{with}\:\:{n}\:{integr}\:{natural}. \\ $$

Question Number 59679 Answers: 3 Comments: 0

Evaluate ∫_0 ^3 (((x^2 +3x)/x^3 ))

$${Evaluate} \\ $$$$\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\left(\frac{{x}^{\mathrm{2}} +\mathrm{3}{x}}{{x}^{\mathrm{3}} }\right) \\ $$$$ \\ $$

Question Number 59659 Answers: 1 Comments: 5

Question Number 59647 Answers: 1 Comments: 1

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