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IntegrationQuestion and Answers: Page 21

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

Question Number 205264 Answers: 1 Comments: 0

pls how to calculate this? ∫_(1/2) ^1 ((ln(x+1))/x)dx

$$\boldsymbol{{pls}}\:\boldsymbol{{how}}\:\boldsymbol{{to}}\:\boldsymbol{{calculate}}\:\boldsymbol{{this}}? \\ $$$$\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \frac{\boldsymbol{{ln}}\left(\boldsymbol{{x}}+\mathrm{1}\right)}{\boldsymbol{{x}}}\boldsymbol{{dx}} \\ $$

Question Number 205248 Answers: 1 Comments: 0

∫_0 ^π ((x^2 cos^2 (x)−xsin(x)−cos(x)−1)/((1+xsin(x))^2 ))dx

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

Question Number 205361 Answers: 1 Comments: 0

Question Number 205245 Answers: 1 Comments: 0

calculate ∫((3xdx)/( (√(1−x^4 )))) plsssssss

$$\boldsymbol{{calculate}} \\ $$$$\:\:\: \\ $$$$\int\frac{\mathrm{3}\boldsymbol{{xdx}}}{\:\sqrt{\mathrm{1}−\boldsymbol{{x}}^{\mathrm{4}} }} \\ $$$$\boldsymbol{{plsssssss}} \\ $$

Question Number 205216 Answers: 0 Comments: 0

∫ ((arccos^3 x)/( (√(1−x^3 )))) dx =?

$$\:\:\:\:\:\int\:\frac{\mathrm{arccos}\:^{\mathrm{3}} \mathrm{x}}{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{3}} }}\:\mathrm{dx}\:=? \\ $$

Question Number 205163 Answers: 1 Comments: 0

∫_0 ^1 ((sin(lnx))/(lnx))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{sin}\left({lnx}\right)}{{lnx}}{dx} \\ $$

Question Number 205151 Answers: 1 Comments: 0

find ∫_0 ^∞ ((ln^2 x)/(1+x^4 ))dx

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}^{\mathrm{2}} {x}}{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$

Question Number 204992 Answers: 1 Comments: 0

Is there any way to integrate: ∫ (1/( (√(ln(x))))) dx without hitting the Gauss error function or e^t^2 and e^(−t^2 ) ?

$$\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{way}\:\mathrm{to}\:\mathrm{integrate}: \\ $$$$\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{ln}\left({x}\right)}}\:{dx} \\ $$$$\mathrm{without}\:\mathrm{hitting}\:\mathrm{the}\:\mathrm{Gauss}\:\mathrm{error}\:\mathrm{function} \\ $$$$\mathrm{or}\:{e}^{{t}^{\mathrm{2}} } \:\mathrm{and}\:{e}^{−{t}^{\mathrm{2}} } \:? \\ $$

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