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IntegrationQuestion and Answers: Page 244

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

Question Number 59803 Answers: 0 Comments: 3

Question Number 59802 Answers: 0 Comments: 1

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

Question Number 59631 Answers: 2 Comments: 3

1) calculate ∫_0 ^(2π) (dx/(acosx +bsinx)) with a , b reals 2)find also ∫_0 ^(2π) ((cosx dx)/((acosx +bsinx)^2 )) and ∫_0 ^(2π) ((sinx dx)/((acosx +bsinx)^2 )) 3) find the value of ∫_0 ^(2π) (dx/(2cosx +(√3)sinx))

$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dx}}{{acosx}\:+{bsinx}} \\ $$$${with}\:{a}\:,\:{b}\:{reals} \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{cosx}\:{dx}}{\left({acosx}\:+{bsinx}\right)^{\mathrm{2}} }\:\:{and} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sinx}\:{dx}}{\left({acosx}\:+{bsinx}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dx}}{\mathrm{2}{cosx}\:+\sqrt{\mathrm{3}}{sinx}} \\ $$

Question Number 59576 Answers: 0 Comments: 4

let f(x) =∫ (dt/((x+t)(√(t^2 −x^2 )))) 1) determine a explicit form of f(x) 2) determine ∫ (dt/((x+2)(√(t^2 −4)))) and ∫ (dt/((x+1)(√(t^2 −1))))

$${let}\:{f}\left({x}\right)\:=\int\:\:\:\:\:\:\:\frac{{dt}}{\left({x}+{t}\right)\sqrt{{t}^{\mathrm{2}} −{x}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:\int\:\:\:\:\:\frac{{dt}}{\left({x}+\mathrm{2}\right)\sqrt{{t}^{\mathrm{2}} −\mathrm{4}}}\:\:{and}\:\:\int\:\:\:\:\:\:\frac{{dt}}{\left({x}+\mathrm{1}\right)\sqrt{{t}^{\mathrm{2}} −\mathrm{1}}} \\ $$

Question Number 59575 Answers: 1 Comments: 0

find ∫ ((sin(2x))/(1+cos^2 x))dx

$${find}\:\int\:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{cos}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 59563 Answers: 2 Comments: 1

Question Number 59528 Answers: 0 Comments: 5

let f(x) =∫_0 ^1 (dt/(1+xch(t))) with x real 1) determine a explicit form of f(x) 2)find also g(x)=∫_0 ^1 (dt/((1+xch(t))^2 )) 3) calculate ∫_0 ^1 (dt/(1+3ch(t))) and ∫_0 ^1 (dt/((1+3ch(t))^2 ))

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\mathrm{1}+{xch}\left({t}\right)}\:{with}\:{x}\:{real} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dt}}{\left(\mathrm{1}+{xch}\left({t}\right)\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{1}+\mathrm{3}{ch}\left({t}\right)}\:{and}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{\left(\mathrm{1}+\mathrm{3}{ch}\left({t}\right)\right)^{\mathrm{2}} } \\ $$

Question Number 59526 Answers: 1 Comments: 1

calculate ∫_0 ^1 (dx/(2sh(x)+3ch(x)))

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

Question Number 59509 Answers: 2 Comments: 0