Question and Answers Forum

All Questions   Topic List

IntegrationQuestion and Answers: Page 1

Question Number 197821    Answers: 0   Comments: 0

find the value of : Ω = ∫_0 ^( 1) (( ln ( 1+ (1/x^( 2) ) ))/(2 + x^( 2) )) dx = ?

$$ \\ $$$$\:\:\:\:{find}\:{the}\:{value}\:\:{of}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\:\mathrm{ln}\:\left(\:\mathrm{1}+\:\frac{\mathrm{1}}{{x}^{\:\mathrm{2}} }\:\right)}{\mathrm{2}\:+\:{x}^{\:\mathrm{2}} }\:{dx}\:=\:? \\ $$$$ \\ $$

Question Number 197819    Answers: 0   Comments: 0

find the value of : 𝛗 = Ξ£_(n=1) ^∞ (( (βˆ’1)^(nβˆ’1) H_( 2n) )/n) = ? where,H_n =1+(1/2) +(1/3) +...+(1/n)

$$ \\ $$$$\:\:\:\:\:\:{find}\:{the}\:{value}\:{of}\:\:: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\left(βˆ’\mathrm{1}\right)^{{n}βˆ’\mathrm{1}} \:{H}_{\:\mathrm{2}{n}} }{{n}}\:=\:? \\ $$$${where},{H}_{{n}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}}\:+...+\frac{\mathrm{1}}{{n}} \\ $$

Question Number 197802    Answers: 1   Comments: 0

I=∫_(βˆ’2) ^6 ((∣xβˆ’1∣)/(xβˆ’1)) dx =?

$$\:\:\:\mathrm{I}=\underset{βˆ’\mathrm{2}} {\overset{\mathrm{6}} {\int}}\:\frac{\mid\mathrm{x}βˆ’\mathrm{1}\mid}{\mathrm{x}βˆ’\mathrm{1}}\:\mathrm{dx}\:=? \\ $$

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^(βˆ’1) x dx=?

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

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 ^(Ο€/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) )^( βˆ’(5/2)) dxdydz=?

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

Question Number 197376    Answers: 1   Comments: 0

Does anyone know how to prove this? ∫∫∫_V ((dxdydz)/(1+x^4 +y^4 +z^4 )) =((Ξ“^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 ∫_(√(xβˆ’x^2 )) ^(√x) ((x^2 βˆ’y^2 )/x^2 )dydx = ??

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

Question Number 197343    Answers: 0   Comments: 0

calculate ∫_0 ^(Ο€/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_(nβ†’βˆž) ∫_(0 ) ^1 ((nx^(nβˆ’1) )/(1+x))dx = ?

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

Question Number 197239    Answers: 1   Comments: 0

Question Number 197212    Answers: 0   Comments: 1

Is ∫f(x)dx=∫_0 ^x lim_(xβ†’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 βˆ’3x+7))dx

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

Question Number 197190    Answers: 1   Comments: 2

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

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

Question Number 197177    Answers: 0   Comments: 0

find ∫_0 ^(Ο€/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 ∫^( (Ο€/2)) _( 0) ((ln(1+Ξ±sint))/(sint))dt= (Ο€^2 /8)βˆ’(1/2)(arccosΞ±)^2

$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{1}+\alpha\mathrm{sin}{t}\right)}{\mathrm{sin}{t}}{dt}=\:\frac{\pi^{\mathrm{2}} }{\mathrm{8}}βˆ’\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{arccos}\alpha\right)^{\mathrm{2}} \\ $$

Question Number 197024    Answers: 3   Comments: 0

calculate Ξ©= ∫_0 ^( (Ο€/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

  Pg 1      Pg 2      Pg 3      Pg 4      Pg 5      Pg 6      Pg 7      Pg 8      Pg 9      Pg 10   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com