Question and Answers Forum

IntegrationQuestion and Answers: Page 20

Question Number 198731 Answers: 2 Comments: 2

Question Number 198695 Answers: 1 Comments: 0

∫_0 ^∞ ((e^(at) −e^(−at) )/(e^(πt) −e^(−πt) )) dt = ??

$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{e}^{\mathrm{at}} −\mathrm{e}^{−\mathrm{at}} }{\mathrm{e}^{\pi\mathrm{t}} −\mathrm{e}^{−\pi\mathrm{t}} }\:\mathrm{dt}\:\:\:=\:\:\:?? \\ $$

Question Number 198497 Answers: 0 Comments: 0

∫_0 ^∞ ((e^(at) −e^(−at) )/(e^(πt) −e^(−πt) )) dt

$$\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{e}^{\mathrm{at}} −\mathrm{e}^{−\mathrm{at}} }{\mathrm{e}^{\pi\mathrm{t}} −\mathrm{e}^{−\pi\mathrm{t}} }\:\mathrm{dt} \\ $$

Question Number 198496 Answers: 1 Comments: 0

A nice series If , Ω = Σ_(n=2) ^∞ (( 1)/(n^( 2) +n −1)) =(( π tan( aπ ))/( b)) ⇒ find the value of (b/a) = ?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:{A}\:{nice}\:\:{series} \\ $$$$\:\:{If}\:,\:\:\Omega\:=\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\:\frac{\:\mathrm{1}}{{n}^{\:\mathrm{2}} \:+{n}\:−\mathrm{1}}\:=\frac{\:\pi\:{tan}\left(\:{a}\pi\:\right)}{\:{b}} \\ $$$$\:\:\:\:\:\Rightarrow\:{find}\:{the}\:{value}\:{of}\:\:\:\frac{{b}}{{a}}\:=\:? \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$

Question Number 198420 Answers: 1 Comments: 0

Question Number 198419 Answers: 0 Comments: 0

Please Help... ∫∫_S x^2 dydz+y^2 dzdx+2z(xy−x−y)dxdy where S is the surface of the cube. 0≤x≤1, 0≤y≤1, 0≤z≤1

$$\:\:{Please}\:{Help}... \\ $$$$\:\:\int\underset{{S}} {\int}{x}^{\mathrm{2}} {dydz}+{y}^{\mathrm{2}} {dzdx}+\mathrm{2}{z}\left({xy}−{x}−{y}\right){dxdy}\:{where} \\ $$$$\:\:\:{S}\:{is}\:{the}\:{surface}\:{of}\:{the}\:{cube}.\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1},\:\mathrm{0}\leqslant{y}\leqslant\mathrm{1}, \\ $$$$\:\:\:\:\mathrm{0}\leqslant{z}\leqslant\mathrm{1} \\ $$$$ \\ $$

Question Number 198403 Answers: 1 Comments: 0

Question Number 198001 Answers: 0 Comments: 2

∫(e)^((x)^(lnx) ) dx=?

$$\int\left({e}\right)^{\left({x}\right)^{{lnx}} } \:{dx}=? \\ $$

Question Number 197919 Answers: 1 Comments: 0

I_m = ∫_0 ^1 (((⌊2^m x⌋)/3^m ) Σ_(n=m+1) ^∞ ((⌊2^n x⌋)/3^n ))dx then find the value of I = Σ_(m=1) ^∞ I_m = ?

$$\:\:\:\:\:\:\mathrm{I}_{{m}} \:\:\:\:\:=\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\lfloor\mathrm{2}^{{m}} {x}\rfloor}{\mathrm{3}^{{m}} }\:\underset{{n}={m}+\mathrm{1}} {\overset{\infty} {\sum}}\frac{\lfloor\mathrm{2}^{{n}} {x}\rfloor}{\mathrm{3}^{{n}} }\right){dx} \\ $$$$\:\:\:\:\:\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\:\:\:\:\:\:\mathrm{I}\:=\:\:\:\underset{{m}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{I}_{{m}} \:\:=\:\:?\: \\ $$

Question Number 197821 Answers: 1 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: 1 Comments: 0

find the value of : 𝛗 = Σ_(n=1) ^∞ (( (−1)^(n−1) H_( 2n) )/n) = ? where,H_n =1+(1/2) +(1/3) +...+(1/n)

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

Question Number 197802 Answers: 1 Comments: 0

I=∫_(−2) ^6 ((∣x−1∣)/(x−1)) dx =?

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

Question Number 197906 Answers: 1 Comments: 0

S= Σ_(k=1) ^∞ (( Γ^( 2) ( k ))/(k Γ (2k ))) = ? −−−−

$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{S}=\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\:\Gamma^{\:\mathrm{2}} \left(\:{k}\:\right)}{{k}\:\Gamma\:\left(\mathrm{2}{k}\:\right)}\:=\:? \\ $$$$\:\:\:\:\:\:\:\:−−−− \\ $$

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

Pg 15 Pg 16 Pg 17 Pg 18 Pg 19 Pg 20 Pg 21 Pg 22 Pg 23 Pg 24

Contact: info@tinkutara.com