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IntegrationQuestion and Answers: Page 19

Question Number 197190 Answers: 1 Comments: 2

∫_0 ^1 ^3 (√(1−x^7 )) dx − ∫^1 _0 ^7 (√(1−x^3 )) dx = ?

$$\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:^{\mathrm{3}} \sqrt{\mathrm{1}−{x}^{\mathrm{7}} }\:{dx}\:−\:\underset{\mathrm{0}} {\int}^{\mathrm{1}} \:^{\mathrm{7}} \sqrt{\mathrm{1}−{x}^{\mathrm{3}} }\:{dx}\:\:=\:\:? \\ $$

Question Number 197177 Answers: 0 Comments: 0

find ∫_0 ^(π/2) ln^2 (cosx)dx

$${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}^{\mathrm{2}} \left({cosx}\right){dx} \\ $$

Question Number 197111 Answers: 1 Comments: 0

$$\:\:\:\:\:\:\cancel{ } \\ $$

Question Number 197060 Answers: 1 Comments: 1

Prove that ∫^( (π/2)) _( 0) ((ln(1+αsint))/(sint))dt= (π^2 /8)−(1/2)(arccosα)^2

$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{1}+\alpha\mathrm{sin}{t}\right)}{\mathrm{sin}{t}}{dt}=\:\frac{\pi^{\mathrm{2}} }{\mathrm{8}}−\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{arccos}\alpha\right)^{\mathrm{2}} \\ $$

Question Number 197024 Answers: 3 Comments: 0

calculate Ω= ∫_0 ^( (π/2)) sin(x) (√( 1+^ sin(x)cos(x))) dx=?

$$ \\ $$$$\:\:\:\:\:\:{calculate} \\ $$$$\:\Omega=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {sin}\left({x}\right)\:\sqrt{\:\mathrm{1}\overset{} {+}\:{sin}\left({x}\right){cos}\left({x}\right)}\:{dx}=? \\ $$$$ \\ $$

Question Number 196983 Answers: 3 Comments: 1

Question Number 196832 Answers: 0 Comments: 1

∫xe^(1/(2x)) dx=?

$$\int{x}\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{2}{x}}} {dx}=? \\ $$

Question Number 196817 Answers: 1 Comments: 0

Question Number 196688 Answers: 1 Comments: 0

Question Number 196788 Answers: 2 Comments: 0

calculer ∫_0 ^1 (√(1−x^2 )) <erly rolvinst>

$${calculer}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{2}} } \\ $$$$<{erly}\:{rolvinst}> \\ $$$$ \\ $$

Question Number 196557 Answers: 1 Comments: 0

Question Number 196496 Answers: 1 Comments: 0

Question Number 196487 Answers: 1 Comments: 0

∫(sec^4 x−cot^4 x)dx

$$\int\left(\mathrm{sec}\:^{\mathrm{4}} {x}−\mathrm{cot}\:^{\mathrm{4}} {x}\right){dx} \\ $$

Question Number 196459 Answers: 1 Comments: 0

Question Number 196436 Answers: 1 Comments: 0

∫(dx/(x(x^n −1)))

$$\int\frac{{dx}}{{x}\left({x}^{{n}} −\mathrm{1}\right)} \\ $$

Question Number 196435 Answers: 0 Comments: 2

Question Number 196375 Answers: 1 Comments: 1

∫(dx/(x(x^4 −1)))

$$\int\frac{{dx}}{{x}\left({x}^{\mathrm{4}} −\mathrm{1}\right)} \\ $$

Question Number 196277 Answers: 3 Comments: 0

$$\:\:\:\:\:\cancel{\underline{\underbrace{ }}\:} \\ $$

Question Number 196276 Answers: 1 Comments: 0

Question Number 196173 Answers: 1 Comments: 0

Calcul I_a =∫_a ^(1/a) ((lnx)/(1+x^2 ))dx (a>0)

$$\boldsymbol{{Calcul}}\:\boldsymbol{{I}}_{\boldsymbol{{a}}} =\int_{\boldsymbol{{a}}} ^{\frac{\mathrm{1}}{\boldsymbol{{a}}}} \frac{\boldsymbol{{lnx}}}{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}\:\left(\boldsymbol{{a}}>\mathrm{0}\right)\: \\ $$

Question Number 196046 Answers: 0 Comments: 0

∫e^x^2 ln^(24) (x)dx

$$\int{e}^{{x}^{\mathrm{2}} } \:{ln}^{\mathrm{24}} \left({x}\right){dx} \\ $$

Question Number 196037 Answers: 2 Comments: 0

∫ ((sin 2x)/(sin^3 x+cos^3 x)) dx =?

$$\:\:\:\int\:\frac{\mathrm{sin}\:\mathrm{2x}}{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}}\:\mathrm{dx}\:=? \\ $$

Question Number 196013 Answers: 1 Comments: 0

quel est la transformer de Fourier de la fonction suivante: f(x)=e^(−(x^2 /2)) Find the Fourier transform of the following fonction.

$${quel}\:{est}\:{la}\:{transformer}\:{de}\:{Fourier}\:{de}\:{la}\:{fonction} \\ $$$${suivante}: \\ $$$${f}\left({x}\right)=\boldsymbol{{e}}^{−\frac{\boldsymbol{{x}}^{\mathrm{2}} }{\mathrm{2}}} \\ $$$$\boldsymbol{{F}}{ind}\:{the}\:{Fourier}\:{transform}\:{of}\:{the}\: \\ $$$${following}\:{fonction}. \\ $$

Question Number 195997 Answers: 0 Comments: 0

Question Number 195995 Answers: 1 Comments: 0

Δ={(x^ y z), x^2 +y^2 ≤1, x≥0,0<z<y+1} calculer I=∫∫∫_Δ xyzdxdydz please i need help

$$\Delta=\left\{\left(\bar {{x}}\:{y}\:{z}\right),\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \leqslant\mathrm{1},\:{x}\geqslant\mathrm{0},\mathrm{0}<{z}<{y}+\mathrm{1}\right\} \\ $$$${calculer}\:\boldsymbol{{I}}=\int\int\int_{\Delta} {xyzdxdydz} \\ $$$${please}\:{i}\:{need}\:{help} \\ $$

Question Number 195910 Answers: 1 Comments: 0

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