Question and Answers Forum

All Questions Topic List

IntegrationQuestion and Answers: Page 125

Question Number 125505 Answers: 1 Comments: 0

let C={z/∣z∣=1} calculste ∫_C tanz dz

$$\mathrm{let}\:\mathrm{C}=\left\{\mathrm{z}/\mid\mathrm{z}\mid=\mathrm{1}\right\}\:\mathrm{calculste}\:\int_{\mathrm{C}} \mathrm{tanz}\:\mathrm{dz} \\ $$

Question Number 125503 Answers: 0 Comments: 0

explicit f(x)=∫_0 ^(2π) ln(x^2 −2xcosθ +1)dθ (xreal)

$$\mathrm{explicit}\:\:\mathrm{f}\left(\mathrm{x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \mathrm{ln}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2xcos}\theta\:+\mathrm{1}\right)\mathrm{d}\theta\:\:\:\left(\mathrm{xreal}\right) \\ $$

Question Number 125501 Answers: 0 Comments: 0

find the value of Σ_(n=2) ^∞ (((−1)^n (2n+1))/(n^4 −1))

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\sum_{\mathrm{n}=\mathrm{2}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} \left(\mathrm{2n}+\mathrm{1}\right)}{\mathrm{n}^{\mathrm{4}} −\mathrm{1}} \\ $$

Question Number 125500 Answers: 1 Comments: 0

find relation between ∫ f(x)dx and ∫ f^(−1) (x)dx

$$\mathrm{find}\:\mathrm{relation}\:\mathrm{between}\:\int\:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\:\mathrm{and}\:\int\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)\mathrm{dx}\:\: \\ $$

Question Number 125462 Answers: 1 Comments: 0

... ♣advanced calculus♣... ⧫⧫ prove that: I=∫_1 ^( ∞) (((t^4 −6t^2 +1)ln(ln(t)))/((1+t^2 )^3 ))dt=((2G)/π) G : catalan constant...

$$\:\:\:\:\:\:\:\:\:\:\:\:\:...\:\clubsuit{advanced}\:\:{calculus}\clubsuit... \\ $$$$\:\:\:\blacklozenge\blacklozenge\:{prove}\:{that}: \\ $$$$\:\:\:\:\:\mathrm{I}=\int_{\mathrm{1}} ^{\:\infty} \frac{\left({t}^{\mathrm{4}} −\mathrm{6}{t}^{\mathrm{2}} +\mathrm{1}\right){ln}\left({ln}\left({t}\right)\right)}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{3}} }{dt}=\frac{\mathrm{2G}}{\pi} \\ $$$$\:\:\mathrm{G}\::\:\:{catalan}\:\:{constant}... \\ $$

Question Number 125458 Answers: 2 Comments: 0

...advanced calculus... evaluate ::: Σ_(n=2) ^∞ { ((ζ (2n ))/2^( n) ) } =??

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...{advanced}\:\:{calculus}... \\ $$$$\:\:\:\:\:\:\:\:{evaluate}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\left\{\:\frac{\zeta\:\left(\mathrm{2}{n}\:\right)}{\mathrm{2}^{\:{n}} }\:\right\}\:=?? \\ $$$$ \\ $$

Question Number 125440 Answers: 2 Comments: 0

∫((2x^2 −3x−3)/((x−1)(x^2 −2x+5))) dx

$$\:\:\:\:\:\:\:\:\:\:\:\int\frac{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{3}}{\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{5}\right)}\:{dx}\: \\ $$

Question Number 125421 Answers: 2 Comments: 0

∫_0 ^(100) (dx/( (√(x(100−x))))) ?

$$\:\underset{\mathrm{0}} {\overset{\mathrm{100}} {\int}}\:\frac{{dx}}{\:\sqrt{{x}\left(\mathrm{100}−{x}\right)}}\:?\: \\ $$

Question Number 125416 Answers: 2 Comments: 0

∫ (dx/( (√(x(√x)−x^2 )))) ?

$$\int\:\frac{{dx}}{\:\sqrt{{x}\sqrt{{x}}−{x}^{\mathrm{2}} }}\:? \\ $$

Question Number 125390 Answers: 2 Comments: 0

nice calculus... evaluate ::::↷ Ω=∫_0 ^( ∞) (((√x) tan^(−1) (x))/(1+x^2 ))dx=???

$$\:\:\:\:\:\:\:\:{nice}\:\:{calculus}... \\ $$$$\:\:\:\:\:{evaluate}\:::::\curvearrowright \\ $$$$\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{\sqrt{{x}}\:{tan}^{−\mathrm{1}} \left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=??? \\ $$

Question Number 125381 Answers: 0 Comments: 0

F(x) = cos (∫_1 ^x cos (∫_1 ^t sin^3 u du )dy) ((dF(x))/dx) = ?

$$\:{F}\left({x}\right)\:=\:\mathrm{cos}\:\left(\underset{\mathrm{1}} {\overset{{x}} {\int}}\:\mathrm{cos}\:\left(\underset{\mathrm{1}} {\overset{{t}} {\int}}\:\mathrm{sin}\:^{\mathrm{3}} {u}\:{du}\:\right){dy}\right) \\ $$$$\:\frac{{dF}\left({x}\right)}{{dx}}\:=\:?\: \\ $$

Question Number 125346 Answers: 4 Comments: 1

∫ x (√(1−x^4 )) dx??

$$\:\int\:{x}\:\sqrt{\mathrm{1}−{x}^{\mathrm{4}} }\:{dx}?? \\ $$

Question Number 125336 Answers: 2 Comments: 0

... nice calculus ... evaluate : φ=∫_(0 ) ^( 1) x^2 ln(x).ln(1−x)dx =?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:{nice}\:\:{calculus}\:... \\ $$$$\:\:{evaluate}\:: \\ $$$$\:\:\:\phi=\int_{\mathrm{0}\:} ^{\:\mathrm{1}} {x}^{\mathrm{2}} {ln}\left({x}\right).{ln}\left(\mathrm{1}−{x}\right){dx}\:=? \\ $$$$ \\ $$

Question Number 125313 Answers: 3 Comments: 0

β(x)=∫ (x^3 /( (√(1−x^2 )))) dx

$$\:\:\:\beta\left({x}\right)=\int\:\frac{{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:{dx}\: \\ $$

Question Number 125276 Answers: 2 Comments: 0

∫_0 ^1 ((x^9 −1)/(lnx))dx=???

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{{x}^{\mathrm{9}} −\mathrm{1}}{{lnx}}{dx}=??? \\ $$

Question Number 125234 Answers: 0 Comments: 1

calculate ∫_0 ^1 (dx/(x+2+(√(x^2 +x+1))))

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\mathrm{dx}}{\mathrm{x}+\mathrm{2}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}} \\ $$

Question Number 125233 Answers: 0 Comments: 0

calculate u_(nm) =∫_0 ^∞ e^(−nx) ln(1+e^(mx) )dx find Σ_(n≥0 and m≥0) u_(nm)

$$\mathrm{calculate}\:\mathrm{u}_{\mathrm{nm}} =\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{nx}} \mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{mx}} \right)\mathrm{dx} \\ $$$$\mathrm{find}\:\sum_{\mathrm{n}\geqslant\mathrm{0}\:\mathrm{and}\:\mathrm{m}\geqslant\mathrm{0}} \:\:\mathrm{u}_{\mathrm{nm}} \\ $$

Question Number 125194 Answers: 1 Comments: 0

∫ (((1−(√(x^2 +x+1)))^2 )/(x^2 (√(x^2 +x+1)))) dx ?

$$\:\int\:\frac{\left(\mathrm{1}−\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} \:\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}\:{dx}\:? \\ $$

Question Number 125187 Answers: 1 Comments: 0

∫ (dx/( (√(sin^3 x)) (√(cos^5 x)))) ?

$$\:\:\int\:\frac{{dx}}{\:\sqrt{\mathrm{sin}\:^{\mathrm{3}} {x}}\:\sqrt{\mathrm{cos}\:^{\mathrm{5}} {x}}}\:? \\ $$

Question Number 125146 Answers: 3 Comments: 0

1)calculate ∫_0 ^(2π) (dθ/(x^2 −2x cosθ +1)) 2) calculate ∫_0 ^(2π) ((cosθ)/((x^2 −2xcosθ +1)^2 ))dθ

$$\left.\mathrm{1}\right)\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{\mathrm{d}\theta}{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}\:\mathrm{cos}\theta\:+\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{\mathrm{cos}\theta}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2xcos}\theta\:+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{d}\theta \\ $$

Question Number 125133 Answers: 3 Comments: 0

... ◂advanced calculus▶... prove that ::: Ω=∫_0 ^( 1) {((cos(log(x))−1)/(log(x)))}dx=((log(2))/2) ...∗adopted from youtube∗... ∗ ∗ youtube solution is not considered ∗ ∗

$$\:\:\:\:\:\:\:\:\:\:\:\:\:...\:\blacktriangleleft{advanced}\:\:\:{calculus}\blacktriangleright... \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}\:::: \\ $$$$\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left\{\frac{{cos}\left({log}\left({x}\right)\right)−\mathrm{1}}{{log}\left({x}\right)}\right\}{dx}=\frac{{log}\left(\mathrm{2}\right)}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:...\ast{adopted}\:{from}\:{youtube}\ast...\:\:\: \\ $$$$\:\ast\:\ast\:{youtube}\:{solution}\:{is}\:{not}\:{considered}\:\ast\:\ast \\ $$$$\:\: \\ $$

Question Number 125125 Answers: 0 Comments: 1

∫_(π/6) ((s^(π/3) inx )/x)dx=?

$$\underset{\frac{\pi}{\mathrm{6}}} {\int}\frac{\overset{\frac{\pi}{\mathrm{3}}} {{s}inx}\:}{{x}}{dx}=? \\ $$

Question Number 125114 Answers: 2 Comments: 1

solve ∫ (dx/((x^3 −1)^2 )) ?

$$\:{solve}\:\int\:\frac{{dx}}{\left({x}^{\mathrm{3}} −\mathrm{1}\right)^{\mathrm{2}} }\:? \\ $$

Question Number 125098 Answers: 1 Comments: 1

...nice calculus ... prove that :: Apery′s constant φ=∫_0 ^( 1) {(4x^2 +4^2 x^2^2 +4^3 x^2^3 +...)((ln^2 (x))/(x(1+x)))}dx =2ζ(3)−1

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:...{nice}\:\:\:{calculus}\:... \\ $$$$\:\:\:\:\:{prove}\:\:{that}\:::\:{Apery}'{s}\:{constant} \\ $$$$\:\:\:\:\:\phi=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left\{\left(\mathrm{4}{x}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} {x}^{\mathrm{2}^{\mathrm{2}} } +\mathrm{4}^{\mathrm{3}} {x}^{\mathrm{2}^{\mathrm{3}} } +...\right)\frac{{ln}^{\mathrm{2}} \left({x}\right)}{{x}\left(\mathrm{1}+{x}\right)}\right\}{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{2}\zeta\left(\mathrm{3}\right)−\mathrm{1} \\ $$

Question Number 125096 Answers: 1 Comments: 0

... nice calculus... suppose :: z =x−iy & (z)^(1/3) =p+iq then find :: A=(((x/p)+(y/q))/(p^2 +q^2 )) =?? note : i=(√(−1))

$$\:\:\:\:\:\:\:\:\:\:\:\:...\:{nice}\:\:\:{calculus}... \\ $$$$\:\:\:\:{suppose}\:::\:{z}\:={x}−{iy}\:\:\&\:\sqrt[{\mathrm{3}}]{{z}}\:={p}+{iq} \\ $$$$\:\:\:{then}\:\:{find}\:::\:\:\:{A}=\frac{\frac{{x}}{{p}}+\frac{{y}}{{q}}}{{p}^{\mathrm{2}} +{q}^{\mathrm{2}} }\:=?? \\ $$$$\:{note}\::\:{i}=\sqrt{−\mathrm{1}} \\ $$

Question Number 125053 Answers: 2 Comments: 1

∫ (dx/( (√(x^2 +3x−4)))) =?

$$\:\:\int\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{4}}}\:=? \\ $$

Pg 120 Pg 121 Pg 122 Pg 123 Pg 124 Pg 125 Pg 126 Pg 127 Pg 128 Pg 129

Terms of Service

Contact: info@tinkutara.com