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Question Number 56060 Answers: 0 Comments: 3

∫e^(−x^2 ) dx as an infinite series.Hence investigate its converge.

$$\int{e}^{−{x}^{\mathrm{2}} } {dx}\:{as}\:{an}\:{infinite}\:{series}.{Hence} \\ $$$${investigate}\:{its}\:{converge}. \\ $$

Question Number 56045 Answers: 1 Comments: 1

Question Number 56042 Answers: 2 Comments: 0

Question Number 56037 Answers: 1 Comments: 5

Question Number 56052 Answers: 1 Comments: 0

Solve following equation for x: x^x^x^n =n with n∈N

$${Solve}\:{following}\:{equation}\:{for}\:{x}: \\ $$$$\boldsymbol{{x}}^{\boldsymbol{{x}}^{\boldsymbol{{x}}^{\boldsymbol{{n}}} } } =\boldsymbol{{n}}\:{with}\:{n}\in\mathbb{N} \\ $$

Question Number 56051 Answers: 2 Comments: 0

Question Number 56053 Answers: 0 Comments: 1

∫_0 ^1 ((x^(17) − 1)/(x^(19) − 1)) dx = ?

$$\underset{\mathrm{0}} {\int}\overset{\mathrm{1}} {\:}\:\:\frac{{x}^{\mathrm{17}} \:−\:\mathrm{1}}{{x}^{\mathrm{19}} \:−\:\mathrm{1}}\:\:{dx}\:\:=\:\:? \\ $$

Question Number 56025 Answers: 2 Comments: 0

Find the probability that a student arranging the letters of the word MATHEMATICS will make all the vowels be together in any arrangement he or she does.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{a}\:\mathrm{student} \\ $$$$\mathrm{arranging}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word} \\ $$$$\mathrm{MATHEMATICS}\:\mathrm{will}\:\mathrm{make}\:\mathrm{all}\:\mathrm{the} \\ $$$$\mathrm{vowels}\:\mathrm{be}\:\mathrm{together}\:\mathrm{in}\:\mathrm{any}\:\mathrm{arrangement} \\ $$$$\mathrm{he}\:\mathrm{or}\:\mathrm{she}\:\mathrm{does}. \\ $$

Question Number 56011 Answers: 2 Comments: 1

Question Number 56005 Answers: 0 Comments: 8

Question Number 55999 Answers: 0 Comments: 1

Question Number 55998 Answers: 1 Comments: 1

find f(x) =∫_0 ^1 arctan(t^2 +xt +1)dt .

$${find}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {arctan}\left({t}^{\mathrm{2}} +{xt}\:+\mathrm{1}\right){dt}\:\:. \\ $$

Question Number 55997 Answers: 0 Comments: 0

calculate ∫_(π/3) ^(π/2) (dx/(x+sinx))

$${calculate}\:\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{dx}}{{x}+{sinx}} \\ $$

Question Number 55996 Answers: 0 Comments: 1

find ∫_(π/3) ^(π/2) (x/(cosx))dx

$${find}\:\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{x}}{{cosx}}{dx}\: \\ $$

Question Number 55995 Answers: 1 Comments: 1

find I =∫ arctan(1−x)dx and J =∫ actan(1+x) dx

$${find}\:{I}\:=\int\:\:{arctan}\left(\mathrm{1}−{x}\right){dx}\:\:{and}\:{J}\:=\int\:{actan}\left(\mathrm{1}+{x}\right)\:{dx} \\ $$

Question Number 55994 Answers: 1 Comments: 0

calculate ∫_0 ^1 arctan(x^2 −x)dx

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

Question Number 55992 Answers: 0 Comments: 2

1 + x + x^2 + . . . + x^(99) =0 need an explanation.

$$\mathrm{1}\:+\:{x}\:+\:{x}^{\mathrm{2}} \:+\:.\:.\:.\:+\:{x}^{\mathrm{99}} =\mathrm{0} \\ $$$${need}\:{an}\:{explanation}. \\ $$

Question Number 55991 Answers: 0 Comments: 2

Question Number 55987 Answers: 0 Comments: 0

Question Number 55980 Answers: 0 Comments: 1

Does the function f(x) = x^x have an antiderivative ? □ yes □ no How this may be proved ?

$${Does}\:{the}\:{function}\:{f}\left({x}\right)\:=\:{x}^{{x}} \:{have} \\ $$$${an}\:{antiderivative}\:? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Box\:{yes}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Box\:{no} \\ $$$${How}\:{this}\:{may}\:{be}\:{proved}\:? \\ $$

Question Number 55971 Answers: 1 Comments: 2

Question Number 55970 Answers: 1 Comments: 0

Question Number 55969 Answers: 1 Comments: 0

solve for x & y x^(logy) = 4 xy = 40

$$\:\:\:\boldsymbol{\mathrm{solve}}\:\:\:\boldsymbol{\mathrm{for}}\:\:\:\boldsymbol{\mathrm{x}}\:\:\:\&\:\:\boldsymbol{\mathrm{y}} \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{logy}}} \:\:\:=\:\:\mathrm{4} \\ $$$$\:\: \\ $$$$\:\:\:\:\boldsymbol{\mathrm{xy}}\:\:\:\:=\:\:\:\:\mathrm{40}\: \\ $$

Question Number 55967 Answers: 0 Comments: 1

Question Number 55954 Answers: 1 Comments: 0

Question Number 55948 Answers: 1 Comments: 0

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