Question and Answers Forum

IntegrationQuestion and Answers: Page 28

Question Number 197783 Answers: 2 Comments: 0

∫((x.arctg(x))/(x^2 +1))dx=?

$$\int\frac{{x}.\boldsymbol{{arctg}}\left(\boldsymbol{{x}}\right)}{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}}\boldsymbol{{dx}}=? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 197767 Answers: 0 Comments: 1

Question Number 197744 Answers: 1 Comments: 0

2∫_0 ^1 tan^(−1) x dx=?

$$\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}} {tan}^{−\mathrm{1}} {x}\:{dx}=? \\ $$

Question Number 197734 Answers: 1 Comments: 0

calcul ∫(lnx)^(√x) dx help pls

$$\boldsymbol{{c}}{alcul}\:\int\left(\boldsymbol{{lnx}}\right)^{\sqrt{\boldsymbol{{x}}}} \boldsymbol{{dx}} \\ $$$$\boldsymbol{{help}}\:\:\boldsymbol{{pls}} \\ $$

Question Number 197637 Answers: 1 Comments: 3

Question Number 197575 Answers: 0 Comments: 0

find ∫_0 ^1 (tanx)^(1/n) dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \left({tanx}\right)^{\frac{\mathrm{1}}{{n}}} {dx} \\ $$

Question Number 197436 Answers: 1 Comments: 0

∫_0 ^(π/2) (dx/(3+tan x)) =?

$$\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{dx}}{\mathrm{3}+\mathrm{tan}\:\mathrm{x}}\:=? \\ $$

Question Number 197431 Answers: 2 Comments: 0

I = ∫_0 ^( ∞) ∫_0 ^( ∞) ∫_0 ^( ∞) ( 1+ x^2 + y^( 2) +z^( 2) )^( −(5/2)) dxdydz=?

$$ \\ $$$$ \\ $$$$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\:\infty} \int_{\mathrm{0}} ^{\:\infty} \int_{\mathrm{0}} ^{\:\infty} \left(\:\mathrm{1}+\:{x}^{\mathrm{2}} \:+\:{y}^{\:\mathrm{2}} +{z}^{\:\mathrm{2}} \right)^{\:−\frac{\mathrm{5}}{\mathrm{2}}} {dxdydz}=? \\ $$$$ \\ $$

Question Number 197376 Answers: 1 Comments: 0

Does anyone know how to prove this? ∫∫∫_V ((dxdydz)/(1+x^4 +y^4 +z^4 )) =((Γ^4 ((1/4)))/4^4 ) where V is the unit cube [0,1]^3 Thankyou.

$${Does}\:{anyone}\:{know}\:{how}\:{to}\:{prove}\:{this}? \\ $$$$\:\:\:\:\:\:\:\:\:\:\int\int\int_{{V}} \:\frac{{dxdydz}}{\mathrm{1}+{x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} }\:=\frac{\Gamma^{\mathrm{4}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\mathrm{4}^{\mathrm{4}} } \\ $$$${where}\:{V}\:{is}\:{the}\:{unit}\:{cube}\:\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{3}} \\ $$$${Thankyou}. \\ $$$$ \\ $$

Question Number 197383 Answers: 0 Comments: 1

evaluate ∫_(1/4) ^1 ∫_(√(x−x^2 )) ^(√x) ((x^2 −y^2 )/x^2 )dydx = ??

$$\:{evaluate}\:\:\int_{\mathrm{1}/\mathrm{4}} ^{\mathrm{1}} \int_{\sqrt{{x}−{x}^{\mathrm{2}} }} ^{\sqrt{{x}}} \frac{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} }{dydx}\:=\:?? \\ $$

Question Number 197343 Answers: 0 Comments: 0

calculate ∫_0 ^(π/2) ln(cosx).ln(sinx)dx

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

Question Number 197292 Answers: 2 Comments: 0

lim_(n→∞) ∫_(0 ) ^1 ((nx^(n−1) )/(1+x))dx = ?

$$\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\int_{\mathrm{0}\:} ^{\mathrm{1}} \frac{{nx}^{{n}−\mathrm{1}} }{\mathrm{1}+{x}}{dx}\:\:=\:\:\:? \\ $$

Question Number 197239 Answers: 1 Comments: 0

Question Number 197212 Answers: 0 Comments: 1

Is ∫f(x)dx=∫_0 ^x lim_(x→t) f(x)dt?

$$\mathrm{Is}\:\int{f}\left({x}\right){dx}=\int_{\mathrm{0}} ^{{x}} \underset{{x}\rightarrow{t}} {\mathrm{lim}}{f}\left({x}\right){dt}? \\ $$

Question Number 197191 Answers: 1 Comments: 0

∫(1/(x^3 −3x+7))dx

$$\int\frac{\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{3}{x}+\mathrm{7}}{dx} \\ $$

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

Pg 23 Pg 24 Pg 25 Pg 26 Pg 27 Pg 28 Pg 29 Pg 30 Pg 31 Pg 32

Contact: info@tinkutara.com