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IntegrationQuestion and Answers: Page 21

Question Number 206248 Answers: 1 Comments: 0

∫(1/( (√((1−t)(2−t)))))dt=...?

$$\int\frac{\mathrm{1}}{\:\sqrt{\left(\mathrm{1}−{t}\right)\left(\mathrm{2}−{t}\right)}}{dt}=...? \\ $$

Question Number 206224 Answers: 3 Comments: 0

find ∫_0 ^1 arctan(x^5 )dx

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left({x}^{\mathrm{5}} \right){dx} \\ $$

Question Number 206200 Answers: 1 Comments: 0

∫((xsinx)/(1−cosx))dx

$$\int\frac{{xsinx}}{\mathrm{1}−{cosx}}{dx} \\ $$

Question Number 206096 Answers: 1 Comments: 0

∫(1/(x^3 (√(x^2 −1)))) .dx

$$\int\frac{\mathrm{1}}{{x}^{\mathrm{3}} \sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:.{dx} \\ $$

Question Number 206078 Answers: 0 Comments: 1

Question Number 206072 Answers: 0 Comments: 0

∫_0 ^π arctan(((ln(sin(x)))/x))dx=...?

$$\int_{\mathrm{0}} ^{\pi} {arctan}\left(\frac{{ln}\left({sin}\left({x}\right)\right)}{{x}}\right){dx}=...? \\ $$

Question Number 206003 Answers: 2 Comments: 0

Question Number 205928 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/(1+x^4 +x^8 ))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{4}} +{x}^{\mathrm{8}} } \\ $$

Question Number 205935 Answers: 1 Comments: 0

∫∫_D (4y^2 sin(xy))dxdy = ??? D: x=y x=0 y=(√(π/2)) 0≤x≤y 0≤y≤(√(π/2))

$$\int\underset{{D}} {\int}\left(\mathrm{4}{y}^{\mathrm{2}} {sin}\left({xy}\right)\right){dxdy}\:\:=\:??? \\ $$$${D}:\:\:\:\:\:\:\:{x}={y}\:\:\:\:\:\:{x}=\mathrm{0}\:\:\:\:\:\:\:{y}=\sqrt{\frac{\pi}{\mathrm{2}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\leqslant{y}\:\:\:\:\:\:\:\mathrm{0}\leqslant{y}\leqslant\sqrt{\frac{\pi}{\mathrm{2}}} \\ $$

Question Number 205910 Answers: 0 Comments: 0

Resuelve la siguiente integral I = ∫(x/(sinh^2 (x)∙ln (sinh (x)) − x∙sinh (x)∙cosh (x))) dx

$${Resuelve}\:{la}\:{siguiente}\:{integral} \\ $$$${I}\:=\:\int\frac{{x}}{\mathrm{sinh}^{\mathrm{2}} \left({x}\right)\centerdot\mathrm{ln}\:\left(\mathrm{sinh}\:\left({x}\right)\right)\:−\:{x}\centerdot\mathrm{sinh}\:\left({x}\right)\centerdot\mathrm{cosh}\:\left({x}\right)}\:{dx} \\ $$

Question Number 205873 Answers: 1 Comments: 0

∫_0 ^π (1/π^2 ) (x/( (√(1+sin^3 x ))))[(3πcosx+4sinx)sin^2 x+4]dx

$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{1}}{\pi^{\mathrm{2}} }\:\frac{{x}}{\:\sqrt{\mathrm{1}+\mathrm{sin}^{\mathrm{3}} {x}\:}}\left[\left(\mathrm{3}\pi\mathrm{cos}{x}+\mathrm{4sin}{x}\right)\mathrm{sin}^{\mathrm{2}} {x}+\mathrm{4}\right]{dx}\:\:\: \\ $$

Question Number 205826 Answers: 0 Comments: 0

f_([0;3]) (x)>0 f(0)=3 f(3)=8 ∫^3 _0 (([f′(x)]^2 )/(f(x)+1))dx = (4/3) f(2)=¿

$$\underset{\left[\mathrm{0};\mathrm{3}\right]} {{f}}\left({x}\right)>\mathrm{0} \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{3} \\ $$$${f}\left(\mathrm{3}\right)=\mathrm{8} \\ $$$$\underset{\mathrm{0}} {\int}^{\mathrm{3}} \frac{\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{{f}\left({x}\right)+\mathrm{1}}{dx}\:=\:\frac{\mathrm{4}}{\mathrm{3}} \\ $$$${f}\left(\mathrm{2}\right)=¿ \\ $$

Question Number 205750 Answers: 2 Comments: 3

∫_0 ^(+∞) (1/(1+e^(2x) ))dx=?

$$\int_{\mathrm{0}} ^{+\infty} \frac{\mathrm{1}}{\mathrm{1}+{e}^{\mathrm{2}{x}} }{dx}=? \\ $$

Question Number 205725 Answers: 1 Comments: 0

Question Number 205625 Answers: 1 Comments: 0

∫_0 ^1 (√(1−x^4 ))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 205599 Answers: 1 Comments: 1

laplace transform... L { sin((√t) )} =? −−−−

$$ \\ $$$$\:{laplace}\:{transform}... \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\mathscr{L}\:\left\{\:\:{sin}\left(\sqrt{{t}}\:\right)\right\}\:=? \\ $$$$−−−− \\ $$

Question Number 205590 Answers: 0 Comments: 2

J=∫_0 ^1 (√(1−x^4 ))dx

$${J}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 205558 Answers: 1 Comments: 0

∫_0 ^(π/2) ((sin^2 4θ )/(sin^2 θ ))dθ = ?

$$\:\:\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \:\frac{\mathrm{sin}^{\mathrm{2}} \mathrm{4}\theta\:}{\mathrm{sin}^{\mathrm{2}} \theta\:}{d}\theta\:\:=\:\:\:? \\ $$

Question Number 205506 Answers: 1 Comments: 0

∫_0 ^1 (√(1−x^4 ))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 205335 Answers: 0 Comments: 0

∫((ax+b)/((x^2 −cx+d)^n ))dx

$$\int\frac{{ax}+{b}}{\left({x}^{\mathrm{2}} −{cx}+{d}\right)^{{n}} }{dx} \\ $$

Question Number 205318 Answers: 0 Comments: 0

]^(]^ ]∡)

$$\left.\overset{\left.\overset{} {\right]}\left.\right]\measuredangle} {\right]} \\ $$

Question Number 205315 Answers: 1 Comments: 0

Question Number 205294 Answers: 1 Comments: 0

∫((3x−x^3 ))^(1/3) dx

$$\int\sqrt[{\mathrm{3}}]{\mathrm{3}{x}−{x}^{\mathrm{3}} }{dx} \\ $$

Question Number 205284 Answers: 0 Comments: 0

Question Number 205279 Answers: 1 Comments: 0

∫^(π/2) _(-π/2) ((8(√2)cosx)/((1+e^(sinx) )(1+sin^4 x)))dx=aπ+blog(3+2(√2)) then find a+b

$$\underset{-\pi/\mathrm{2}} {\int}^{\pi/\mathrm{2}} \frac{\mathrm{8}\sqrt{\mathrm{2}}{cosx}}{\left(\mathrm{1}+\overset{{sinx}} {{e}}\right)\left(\mathrm{1}+{si}\overset{\mathrm{4}} {{n}x}\right)}{dx}={a}\pi+{blog}\left(\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}\right)\:{then}\:{find}\:{a}+{b} \\ $$

Question Number 205269 Answers: 2 Comments: 0

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