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Question Number 45783 Answers: 0 Comments: 1

sec(π/7)=((48−(√(3a)))/(36))

$${sec}\frac{\pi}{\mathrm{7}}=\frac{\mathrm{48}−\sqrt{\mathrm{3}{a}}}{\mathrm{36}} \\ $$

Question Number 45735 Answers: 2 Comments: 1

∫_α ^β (1/((x−α)(β−x)))dx =? β>α

$$\int_{\alpha} ^{\beta} \frac{\mathrm{1}}{\left({x}−\alpha\right)\left(\beta−{x}\right)}{dx}\:\:=?\:\:\:\beta>\alpha \\ $$

Question Number 45730 Answers: 2 Comments: 3

Question Number 45753 Answers: 1 Comments: 0

Question Number 45721 Answers: 0 Comments: 3

Integrate sin (x^2 )dx

$$\:{Integrate}\:\mathrm{sin}\:\left({x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 45719 Answers: 1 Comments: 0

Question Number 45720 Answers: 2 Comments: 5

𝚺_(r = 1) ^n (r + 1)^3

$$\underset{\boldsymbol{\mathrm{r}}\:=\:\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\boldsymbol{\sum}}}\:\:\left(\boldsymbol{\mathrm{r}}\:+\:\mathrm{1}\right)^{\mathrm{3}} \\ $$

Question Number 45712 Answers: 0 Comments: 3

prove that : (√2) is irrationl number

$$\mathrm{prove}\:\mathrm{that}\:: \\ $$$$\sqrt{\mathrm{2}}\:\mathrm{is}\:\mathrm{irrationl}\:\mathrm{number} \\ $$

Question Number 45707 Answers: 0 Comments: 0

Question Number 45706 Answers: 1 Comments: 0

Question Number 45705 Answers: 0 Comments: 3

Question Number 45690 Answers: 1 Comments: 1

Question Number 45688 Answers: 1 Comments: 2

∫(1/(sinxcos^2 x))dx=?

$$\int\frac{\mathrm{1}}{{sinxcos}^{\mathrm{2}} {x}}{dx}=? \\ $$

Question Number 45681 Answers: 1 Comments: 0

Question Number 45673 Answers: 1 Comments: 1

Question Number 45670 Answers: 1 Comments: 1

∫cos^(−1) (sinx)dx=?

$$\int{cos}^{−\mathrm{1}} \left({sinx}\right){dx}=? \\ $$

Question Number 45669 Answers: 2 Comments: 0

∫tan^(−1) (√((1−sinx)/(1+sinx))) dx=?

$$\int{tan}^{−\mathrm{1}} \sqrt{\frac{\mathrm{1}−{sinx}}{\mathrm{1}+{sinx}}}\:{dx}=? \\ $$

Question Number 45654 Answers: 0 Comments: 1

Question Number 45649 Answers: 1 Comments: 1

Let consider A(3,5), B(6,4) and C(3,−2), d : x−5y+7=0 Consider a dot D such as ABCD is a trapezium and (AD) and (BC) are parallel lines. Q1) Give the equation of the line which contains the point D. Q2) Considering that the trapezium should be convex, are all the points D of the lines correct for the Trapezium ? Which ones are ? Give a proof. I have some difficulties to anzwer the question n°2, could someone please, help me. Thank you. H.T.

$$\mathrm{Let}\:\mathrm{consider}\:\mathrm{A}\left(\mathrm{3},\mathrm{5}\right),\:\mathrm{B}\left(\mathrm{6},\mathrm{4}\right)\:\mathrm{and}\:\mathrm{C}\left(\mathrm{3},−\mathrm{2}\right), \\ $$$$\mathrm{d}\::\:{x}−\mathrm{5}{y}+\mathrm{7}=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Consider}\:\mathrm{a}\:\mathrm{dot}\:\mathrm{D}\:\mathrm{such}\:\mathrm{as}\:\mathrm{ABCD}\:\mathrm{is}\:\mathrm{a}\:\mathrm{trapezium} \\ $$$$\mathrm{and}\:\left(\mathrm{AD}\right)\:\mathrm{and}\:\left(\mathrm{BC}\right)\:\mathrm{are}\:\mathrm{parallel}\:\mathrm{lines}. \\ $$$$ \\ $$$$\left.\mathrm{Q1}\right)\:\:\:\mathrm{Give}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mathrm{which} \\ $$$$\mathrm{contains}\:\mathrm{the}\:\mathrm{point}\:\mathrm{D}. \\ $$$$ \\ $$$$\left.\mathrm{Q2}\right)\:\:\:\mathrm{Considering}\:\mathrm{that}\:\mathrm{the}\:\mathrm{trapezium} \\ $$$$\mathrm{should}\:\mathrm{be}\:\mathrm{convex},\:\mathrm{are}\:\mathrm{all}\:\mathrm{the}\:\mathrm{points}\:\mathrm{D}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{lines}\:\mathrm{correct}\:\mathrm{for}\:\mathrm{the}\:\mathrm{Trapezium}\:? \\ $$$$\mathrm{Which}\:\mathrm{ones}\:\mathrm{are}\:? \\ $$$$\mathrm{Give}\:\mathrm{a}\:\mathrm{proof}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{I}\:\mathrm{have}\:\mathrm{some}\:\mathrm{difficulties}\:\mathrm{to}\:\mathrm{anzwer}\:\mathrm{the} \\ $$$$\mathrm{question}\:\mathrm{n}°\mathrm{2},\:\mathrm{could}\:\mathrm{someone}\:\mathrm{please}, \\ $$$$\mathrm{help}\:\mathrm{me}. \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you}. \\ $$$$ \\ $$$$\mathrm{H}.\mathrm{T}. \\ $$

Question Number 45646 Answers: 0 Comments: 2

According to relativistic theory, E^2 = p^2 c^2 +m_0 ^2 c^4 where m_0 is rest mass. For photon E= pc... (m_0 =0 for photon) For electron E=mc^2 ... Unlike photon ,Why p^2 c^2 is neglected in case of electron ?

$${According}\:{to}\:{relativistic}\:{theory}, \\ $$$${E}^{\mathrm{2}} =\:{p}^{\mathrm{2}} {c}^{\mathrm{2}} +{m}_{\mathrm{0}} ^{\mathrm{2}} {c}^{\mathrm{4}} \:{where}\:{m}_{\mathrm{0}} \:{is}\:{rest}\:{mass}. \\ $$$${For}\:{photon}\:{E}=\:{pc}... \\ $$$$\left({m}_{\mathrm{0}} =\mathrm{0}\:{for}\:{photon}\right) \\ $$$${For}\:{electron}\:{E}={mc}^{\mathrm{2}} ... \\ $$$${Unlike}\:{photon}\:,{Why}\:{p}^{\mathrm{2}} {c}^{\mathrm{2}} \:{is}\:{neglected}\:\: \\ $$$${in}\:{case}\:{of}\:{electron}\:? \\ $$

Question Number 45645 Answers: 1 Comments: 0

Question Number 45641 Answers: 2 Comments: 1

Question Number 45639 Answers: 3 Comments: 0

Question Number 45638 Answers: 1 Comments: 0

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

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

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