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Question Number 40664 Answers: 1 Comments: 0

Factorise: x^(19) − x^(17) + x^(10) + x^8 + 1

$$\mathrm{Factorise}:\:\:\:\:\:\mathrm{x}^{\mathrm{19}} \:−\:\mathrm{x}^{\mathrm{17}} \:+\:\mathrm{x}^{\mathrm{10}} \:+\:\mathrm{x}^{\mathrm{8}} \:+\:\mathrm{1} \\ $$

Question Number 40662 Answers: 1 Comments: 5

Question Number 40661 Answers: 0 Comments: 4

1)find g(x)=∫_0 ^(π/2) ln(1−x^2 cos^2 θ)dθ with x from R 2) find the value of ∫_0 ^(π/2) ln(1−2 cos^2 θ)dθ and 3) find the value of A(α)=∫_0 ^(π/2) ln(1−cos^2 α cos^2 θ)dθ

$$\left.\mathrm{1}\right){find}\:\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}−{x}^{\mathrm{2}} {cos}^{\mathrm{2}} \theta\right){d}\theta\:\:{with}\:{x}\:{from}\:{R} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}−\mathrm{2}\:{cos}^{\mathrm{2}} \theta\right){d}\theta\:{and} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\: \\ $$$${A}\left(\alpha\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}−{cos}^{\mathrm{2}} \alpha\:{cos}^{\mathrm{2}} \theta\right){d}\theta\: \\ $$

Question Number 40660 Answers: 0 Comments: 0

let f(t) = ∫_0 ^∞ ((arctan(tcosx))/(1+x^2 ))dx 1) find another form of f(t) 2) calculate ∫_0 ^∞ ((arctan(2cosx))/(1+x^2 ))dx .

$${let}\:{f}\left({t}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({tcosx}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{another}\:{form}\:{of}\:{f}\left({t}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\frac{{arctan}\left(\mathrm{2}{cosx}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:. \\ $$

Question Number 40658 Answers: 0 Comments: 1

find ∫_0 ^(π/4) ((x−1)/(2+cosx))dx .

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{{x}−\mathrm{1}}{\mathrm{2}+{cosx}}{dx}\:. \\ $$

Question Number 40657 Answers: 1 Comments: 0

Question Number 40656 Answers: 1 Comments: 0

(((a 0 0)),((0 a 0)) ) 0 0 a then the value of mod of adjA is

$$\begin{pmatrix}{\mathrm{a}\:\mathrm{0}\:\mathrm{0}}\\{\mathrm{0}\:\mathrm{a}\:\mathrm{0}}\end{pmatrix} \\ $$$$\:\:\:\mathrm{0}\:\mathrm{0}\:\mathrm{a}\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{mod}\:\mathrm{of}\:\mathrm{adjA}\:\mathrm{is} \\ $$$$ \\ $$

Question Number 40640 Answers: 2 Comments: 0

evaluate sin 72^.

$${evaluate} \\ $$$$\mathrm{sin}\:\mathrm{72}\:^{.} \\ $$

Question Number 41351 Answers: 1 Comments: 3

∫_0 ^∞ [(5/e^x )]dx=

$$\int_{\mathrm{0}} ^{\infty} \left[\frac{\mathrm{5}}{\mathrm{e}^{\mathrm{x}} }\right]\mathrm{dx}= \\ $$

Question Number 40637 Answers: 2 Comments: 0

Question Number 40625 Answers: 2 Comments: 0

Question Number 40624 Answers: 0 Comments: 0

let f(x)=∫_0 ^(π/2) ln(((1−xsint)/(1+xsint)))dt . 1) find the value of I = ∫_0 ^(π/2) ln(1−xsint)dt and J = ∫_0 ^(π/2) ln(1+xsint)dt 2) find a simple form of f(x) 3) developp f at integr serie

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\frac{\mathrm{1}−{xsint}}{\mathrm{1}+{xsint}}\right){dt}\:\:. \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{ln}\left(\mathrm{1}−{xsint}\right){dt} \\ $$$${and}\:{J}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}+{xsint}\right){dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$

Question Number 40621 Answers: 2 Comments: 0

let f(x)=∫_0 ^(π/2) ln(1+xcosθ)dθ 1) calculate f(1) 2) find a simple form of f(x) 3) developp f at ontehr serie

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}+{xcos}\theta\right){d}\theta\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left(\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{ontehr}\:{serie} \\ $$

Question Number 40620 Answers: 3 Comments: 0

find ∫ ((x+1)(√(1+x^2 )) +(1+x^2 )(√(x+1)))dx

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

Question Number 40619 Answers: 0 Comments: 2

let f(x)=∫_0 ^(π/2) (dθ/(x +cos^2 θ)) with x>0 . 1) calculate f(x) and f^′ (x) 2) find f^((n)) (x) and f^((n)) (0) 3) developp f at integr serie.

$${let}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{d}\theta}{{x}\:\:+{cos}^{\mathrm{2}} \theta}\:\:{with}\:{x}>\mathrm{0}\:. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right)\:{and}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 40615 Answers: 1 Comments: 2

Question Number 40610 Answers: 1 Comments: 0

Question Number 40594 Answers: 1 Comments: 1

Question Number 40587 Answers: 0 Comments: 1

find ∫e^x lnx dx

$$\boldsymbol{\mathrm{find}}\:\int\boldsymbol{\mathrm{e}}^{\boldsymbol{{x}}} \boldsymbol{\mathrm{ln}{x}}\:\boldsymbol{\mathrm{d}{x}} \\ $$

Question Number 40583 Answers: 2 Comments: 0

2^(√x) = x find x

$$\mathrm{2}^{\sqrt{{x}}} =\:{x} \\ $$$${find}\:{x} \\ $$

Question Number 40581 Answers: 1 Comments: 2

Question Number 40580 Answers: 0 Comments: 3

find ∫_0 ^∞ ((ln(1+ix))/(x^3 +8))dx

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{1}+{ix}\right)}{{x}^{\mathrm{3}} \:+\mathrm{8}}{dx} \\ $$$$ \\ $$

Question Number 40591 Answers: 1 Comments: 1

Question Number 40569 Answers: 0 Comments: 0

Question Number 40551 Answers: 1 Comments: 5

Question Number 40550 Answers: 1 Comments: 0

if three numbers are drawn at random successively without replacement from a set S={1,2,......10}then probability that the minimum of the choosen number is 3 or their maximum is 7 Answer=((11)/(40))

$$\mathrm{if}\:\mathrm{three}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{at}\:\mathrm{random} \\ $$$$\mathrm{successively}\:\mathrm{without}\:\mathrm{replacement}\:\mathrm{from} \\ $$$$\mathrm{a}\:\mathrm{set}\:\mathrm{S}=\left\{\mathrm{1},\mathrm{2},......\mathrm{10}\right\}\mathrm{then}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{choosen}\:\mathrm{number}\:\mathrm{is} \\ $$$$\mathrm{3}\:\mathrm{or}\:\mathrm{their}\:\mathrm{maximum}\:\mathrm{is}\:\mathrm{7}\:\:\:\:\:\:\:\: \\ $$$$\:\mathrm{Answer}=\frac{\mathrm{11}}{\mathrm{40}} \\ $$

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