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AllQuestion and Answers: Page 1633

Question Number 45635 Answers: 0 Comments: 2

1)find f(x)=∫_0 ^1 ln(1+xt^3 )dt with ∣x∣<1 2) calculate ∫_0 ^1 ln(2+t^3 )dt .

$$\left.\mathrm{1}\right){find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{xt}^{\mathrm{3}} \right){dt}\:\:{with}\:\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{2}+{t}^{\mathrm{3}} \right){dt}\:. \\ $$

Question Number 45634 Answers: 0 Comments: 0

1)find ∫ ln(1−x^6 )dx 2) calculate ∫_0 ^1 ln(1−x^6 )dx

$$\left.\mathrm{1}\right){find}\:\int\:{ln}\left(\mathrm{1}−{x}^{\mathrm{6}} \right){dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{x}^{\mathrm{6}} \right){dx} \\ $$

Question Number 45632 Answers: 0 Comments: 2

1)find ∫ ln(1+x^3 )dx 2) calculate ∫_0 ^1 ln(1+x^3 )ex

$$\left.\mathrm{1}\right){find}\:\int\:{ln}\left(\mathrm{1}+{x}^{\mathrm{3}} \right){dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{x}^{\mathrm{3}} \right){ex} \\ $$

Question Number 45630 Answers: 2 Comments: 0

Question Number 45610 Answers: 0 Comments: 1

Question Number 45609 Answers: 0 Comments: 3

Question Number 45608 Answers: 1 Comments: 0

Question Number 45602 Answers: 2 Comments: 0

Question Number 45601 Answers: 0 Comments: 0

Question Number 45600 Answers: 0 Comments: 2

find f(x,y) =∫_0 ^(π/2) ln(x+y sinθ)dθ with ∣y∣<∣x∣ 2) find f(2,3) 3)find f((√2),(√3)) .

$${find}\:{f}\left({x},{y}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({x}+{y}\:{sin}\theta\right){d}\theta\:\:{with}\:\:\mid{y}\mid<\mid{x}\mid \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}\left(\mathrm{2},\mathrm{3}\right) \\ $$$$\left.\mathrm{3}\right){find}\:{f}\left(\sqrt{\mathrm{2}},\sqrt{\mathrm{3}}\right)\:. \\ $$

Question Number 45599 Answers: 0 Comments: 1

1) calculate A_n = ∫_0 ^n (((−1)^([x]) )/(2x+1−[x]))dx 2) find lim_(n→+∞) A_n 3) study the serie Σ A_n

$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\mathrm{2}{x}+\mathrm{1}−\left[{x}\right]}{dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} {A}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{study}\:{the}\:{serie}\:\:\Sigma\:{A}_{{n}} \\ $$

Question Number 45598 Answers: 0 Comments: 1

calculate Σ_(n=1) ^∞ ((2n+1)/(n^2 (4n^2 −1)))

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

Question Number 45594 Answers: 0 Comments: 1

calculate Σ_(n=1) ^∞ (1/((4n^2 −1)^2 ))

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\mathrm{1}}{\left(\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 45592 Answers: 0 Comments: 0

Question Number 45589 Answers: 0 Comments: 0

pl help me sir mathtype 6c seril key

$$\mathrm{pl}\:\mathrm{help}\:\mathrm{me}\:\mathrm{sir}\:\mathrm{mathtype}\:\mathrm{6c}\:\:\mathrm{seril}\:\mathrm{key} \\ $$

Question Number 45585 Answers: 1 Comments: 6

prove that1^3 +2^3 +3^3 +...+n^3 =((n^2 (n+1)^2 )/4) for every natural number n

$$\mathrm{prove}\:\mathrm{that1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +\mathrm{3}^{\mathrm{3}} +...+\mathrm{n}^{\mathrm{3}} =\frac{\mathrm{n}^{\mathrm{2}} \left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{4}}\:\mathrm{for}\:\mathrm{every} \\ $$$$\mathrm{natural}\:\mathrm{number}\:\boldsymbol{\mathrm{n}} \\ $$

Question Number 45575 Answers: 2 Comments: 4

Question Number 45565 Answers: 2 Comments: 0

If ax^2 +by^2 +2hxy+2gx+2fy+c=0 be the equation of an ellipse, find coordinates of center of ellipse. Q.45506 (another solution)

$${If}\:\:\boldsymbol{{ax}}^{\mathrm{2}} +\boldsymbol{{by}}^{\mathrm{2}} +\mathrm{2}\boldsymbol{{hxy}}+\mathrm{2}\boldsymbol{{gx}}+\mathrm{2}\boldsymbol{{fy}}+\boldsymbol{{c}}=\mathrm{0} \\ $$$${be}\:{the}\:{equation}\:{of}\:{an}\:{ellipse},\:{find} \\ $$$${coordinates}\:{of}\:{center}\:{of}\:{ellipse}. \\ $$$${Q}.\mathrm{45506}\:\:\left({another}\:{solution}\right) \\ $$

Question Number 45563 Answers: 0 Comments: 0

Question Number 45561 Answers: 0 Comments: 2

Question Number 45555 Answers: 1 Comments: 1

Prove that points (4,−1,3) & (5,−1,4) lies on same side of the plane x+y+z=7.

$${Prove}\:{that}\:{points}\:\left(\mathrm{4},−\mathrm{1},\mathrm{3}\right)\:\&\:\left(\mathrm{5},−\mathrm{1},\mathrm{4}\right) \\ $$$${lies}\:{on}\:{same}\:{side}\:{of}\:{the}\:{plane}\:{x}+{y}+{z}=\mathrm{7}. \\ $$

Question Number 45546 Answers: 2 Comments: 1

Simplify: (((√5) + 2))^(1/3) + (((√5) − 2))^(1/3)

$$\mathrm{Simplify}:\:\:\:\:\:\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{5}}\:\:+\:\:\mathrm{2}}\:\:\:+\:\:\:\:\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{5}}\:\:−\:\mathrm{2}}\:\: \\ $$

Question Number 45539 Answers: 1 Comments: 2

Question Number 45543 Answers: 0 Comments: 0

Question Number 45527 Answers: 0 Comments: 2

Question Number 45520 Answers: 0 Comments: 1

let a>0 and b>0 calculate ∫ (√(acos^2 θ +bsin^2 θ))dπ 2) find ∫_(π/4) ^(π/2) (√(2cos^2 θ +3 sin^2 θ))dθ .

$${let}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0}\:{calculate}\:\int\:\sqrt{{acos}^{\mathrm{2}} \theta\:+{bsin}^{\mathrm{2}} \theta}{d}\pi \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{2}}} \sqrt{\mathrm{2}{cos}^{\mathrm{2}} \theta\:+\mathrm{3}\:{sin}^{\mathrm{2}} \theta}{d}\theta\:. \\ $$

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