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... mathematical analysis... if ′′ f ′′ is Reimann integrable function on [a , b ] , then prove:: lim_(t→∞ ) {∫_a ^( b) f(x)cos(tx)dx }=0 ..Reimann−Lebesgue theorem...

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:{mathematical}\:\:{analysis}... \\ $$$$\:\:{if}\:''\:\:{f}\:\:\:''\:\:{is}\:\mathscr{R}{eimann}\:{integrable} \\ $$$$\:\:\:{function}\:\:{on}\:\left[{a}\:,\:{b}\:\right]\:,\:{then}\:{prove}:: \\ $$$$\:\:\:\:\: \\ $$$$\:\:{lim}_{{t}\rightarrow\infty\:} \left\{\int_{{a}} ^{\:{b}} {f}\left({x}\right){cos}\left({tx}\right){dx}\:\right\}=\mathrm{0} \\ $$$$\:\:..\mathscr{R}{eimann}−\mathscr{L}{ebesgue}\:\:{theorem}... \\ $$$$ \\ $$

Question Number 128542 Answers: 1 Comments: 0

∫ (((x^4 −x)^(1/4) )/x^5 ) dx =?

$$\:\int\:\frac{\left(\mathrm{x}^{\mathrm{4}} −\mathrm{x}\right)^{\mathrm{1}/\mathrm{4}} }{\mathrm{x}^{\mathrm{5}} }\:\mathrm{dx}\:=? \\ $$

Question Number 128540 Answers: 1 Comments: 1

If f(x)=lim_(x→∞) ((x^n −x^(−n) )/(x^n +x^(−n) )) ,x>1 then ∫ ((xf(x) ln (x+(√(1+x^2 )) ))/( (√(1+x^2 )))) dx =?

$$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{n}} −\mathrm{x}^{−\mathrm{n}} }{\mathrm{x}^{\mathrm{n}} +\mathrm{x}^{−\mathrm{n}} }\:,\mathrm{x}>\mathrm{1} \\ $$$$\mathrm{then}\:\int\:\frac{\mathrm{xf}\left(\mathrm{x}\right)\:\mathrm{ln}\:\left(\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\right)}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:=? \\ $$

Question Number 128529 Answers: 1 Comments: 2

Question Number 128511 Answers: 1 Comments: 0

H=∫ ((2017x^(2016) +2018x^(2017) )/(1+x^(4034) +2x^(4035) +x^(4036) )) dx

$$\:\mathcal{H}=\int\:\frac{\mathrm{2017x}^{\mathrm{2016}} +\mathrm{2018x}^{\mathrm{2017}} }{\mathrm{1}+\mathrm{x}^{\mathrm{4034}} +\mathrm{2x}^{\mathrm{4035}} +\mathrm{x}^{\mathrm{4036}} }\:\mathrm{dx}\: \\ $$

Question Number 128499 Answers: 1 Comments: 0

find u_n =∫_1 ^∞ (([ne^(−x) ])/n^3 )dx

$$\mathrm{find}\:\:\mathrm{u}_{\mathrm{n}} =\int_{\mathrm{1}} ^{\infty} \:\:\frac{\left[\mathrm{ne}^{−\mathrm{x}} \right]}{\mathrm{n}^{\mathrm{3}} }\mathrm{dx} \\ $$

Question Number 128495 Answers: 0 Comments: 0

find ∫_0 ^∞ ((sinx)/([x]))dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{sinx}}{\left[\mathrm{x}\right]}\mathrm{dx} \\ $$

Question Number 128471 Answers: 2 Comments: 0

... calculus ... Φ=^? ∫_0 ^( 1) (ln(x))^2 ln((√(−ln(x))) dx

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:\:{calculus}\:... \\ $$$$\:\:\:\:\:\:\:\Phi\overset{?} {=}\int_{\mathrm{0}} ^{\:\mathrm{1}} \left({ln}\left({x}\right)\right)^{\mathrm{2}} {ln}\left(\sqrt{−{ln}\left({x}\right)}\:{dx}\right. \\ $$

Question Number 128417 Answers: 1 Comments: 0

η = ∫_0 ^( 1) x^3 (1−x^3 )^(n−1) dx

$$\:\:\:\:\:\:\:\:\:\eta\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{x}^{\mathrm{3}} \:\left(\mathrm{1}−\mathrm{x}^{\mathrm{3}} \right)^{\mathrm{n}−\mathrm{1}} \:\mathrm{dx}\: \\ $$

Question Number 128408 Answers: 1 Comments: 0

ρ = ∫ ((sin (4x))/(sin^4 (x)+cos^4 (x))) dx

$$\rho\:=\:\int\:\frac{\mathrm{sin}\:\left(\mathrm{4}{x}\right)}{\mathrm{sin}\:^{\mathrm{4}} \left({x}\right)+\mathrm{cos}\:^{\mathrm{4}} \left({x}\right)}\:{dx}\: \\ $$

Question Number 128385 Answers: 1 Comments: 0

∫_1 ^( π) determinant ((x^3 ,(lnx),(sinx)),((3x^2 ),(1/x),(cosx)),(6,(2x^(−3) ),(−cosx)))dx =?

$$\int_{\mathrm{1}} ^{\:\pi} \begin{vmatrix}{\mathrm{x}^{\mathrm{3}} }&{\mathrm{lnx}}&{\mathrm{sinx}}\\{\mathrm{3x}^{\mathrm{2}} }&{\frac{\mathrm{1}}{\mathrm{x}}}&{\mathrm{cosx}}\\{\mathrm{6}}&{\mathrm{2x}^{−\mathrm{3}} }&{−\mathrm{cosx}}\end{vmatrix}\mathrm{dx}\:=?\: \\ $$

Question Number 128373 Answers: 1 Comments: 0

∫_0 ^1 x^(3/2) (1−x)^(1/2) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{\frac{\mathrm{3}}{\mathrm{2}}} \left(\mathrm{1}−{x}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:{dx} \\ $$

Question Number 128334 Answers: 1 Comments: 0

Ω = ∫ (x^2 /( (√((a+bx^2 )^5 )))) dx ; where : a; b >0

$$\Omega\:=\:\int\:\frac{\mathrm{x}^{\mathrm{2}} }{\:\sqrt{\left(\mathrm{a}+\mathrm{bx}^{\mathrm{2}} \right)^{\mathrm{5}} }}\:\mathrm{dx}\:;\:\mathrm{where}\::\:\mathrm{a};\:\mathrm{b}\:>\mathrm{0}\: \\ $$

Question Number 128346 Answers: 2 Comments: 0

Question Number 128316 Answers: 1 Comments: 0

nice calculus Ω= ∫_0 ^( ∞) ((sin^3 (x))/x^2 )dx=?

$$\:\:\:\:\:\:\:\:\:\:\:\:{nice}\:\:{calculus} \\ $$$$\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}^{\mathrm{3}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx}=? \\ $$$$ \\ $$

Question Number 128285 Answers: 1 Comments: 0

cos ((π/7))−cos (((2π)/7))+cos (((3π)/7)) =?

$$\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{7}}\right)−\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:=? \\ $$

Question Number 128276 Answers: 1 Comments: 0

∫_e^2 ^( ∞) (dx/(x^3 ln x)) ?

$$\:\int_{{e}^{\mathrm{2}} } ^{\:\infty} \:\frac{{dx}}{{x}^{\mathrm{3}} \:\mathrm{ln}\:{x}}\:? \\ $$

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