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Question Number 116299 Answers: 0 Comments: 0

... advanced math ... evaluate that : Ω=∫_0 ^( 1) [(1/(ln(x))) +(1/(1−x)) ]^2 dx=??? m.n

$$\:\:\:...\:\:{advanced}\:\:{math}\:... \\ $$$$\:\:\:\:\:\:\:{evaluate}\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left[\frac{\mathrm{1}}{{ln}\left({x}\right)}\:+\frac{\mathrm{1}}{\mathrm{1}−{x}}\:\right]^{\mathrm{2}} {dx}=??? \\ $$$$\:\:\:\:\:\:\:{m}.{n} \\ $$

Question Number 116290 Answers: 0 Comments: 1

Question Number 116301 Answers: 2 Comments: 0

What is the condition for a given line to 1) intersect a curve 2) be a tangent to a curve 3) not to intersect a curve

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{condition}\:\mathrm{for}\:\mathrm{a} \\ $$$$\mathrm{given}\:\mathrm{line}\:\mathrm{to}\:\: \\ $$$$\left.\mathrm{1}\right)\:\mathrm{intersect}\:\mathrm{a}\:\mathrm{curve} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{be}\:\mathrm{a}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{a}\:\mathrm{curve} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{not}\:\mathrm{to}\:\mathrm{intersect}\:\mathrm{a}\:\mathrm{curve}\: \\ $$

Question Number 116281 Answers: 2 Comments: 0

Prove that sin 10° sin 30° sin 50° sin 70°.

$$\mathrm{Prove}\:\mathrm{that}\:\:\:\mathrm{sin}\:\mathrm{10}°\:\mathrm{sin}\:\mathrm{30}°\:\mathrm{sin}\:\mathrm{50}°\:\mathrm{sin}\:\mathrm{70}°. \\ $$

Question Number 116284 Answers: 3 Comments: 0

... calculus I ... evaluate : I := ∫_0 ^( (π/3)) log(1+(√3) tan(x))dx=???

$$\:\:\:\:\:\:\:\:\:\:\:\:\:...\:\:{calculus}\:{I}\:... \\ $$$$\:\:\:\:\:{evaluate}\::\: \\ $$$$ \\ $$$$\:\:\:\:\:\mathrm{I}\::=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{3}}} {log}\left(\mathrm{1}+\sqrt{\mathrm{3}}\:{tan}\left({x}\right)\right){dx}=??? \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 116279 Answers: 2 Comments: 0

∫ ((xe^x )/((x+1)^2 ))dx

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

Question Number 116276 Answers: 0 Comments: 0

Question Number 116272 Answers: 1 Comments: 0

∫_0 ^(π/2) ln(x^2 +ln^2 (cos(x)))dx=πln(ln(2)) posted Quation not solved yet i hop someon Giv idea for this one thank you

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({x}^{\mathrm{2}} +{ln}^{\mathrm{2}} \left({cos}\left({x}\right)\right)\right){dx}=\pi{ln}\left({ln}\left(\mathrm{2}\right)\right) \\ $$$${posted}\:{Quation}\: \\ $$$${not}\:{solved}\:{yet}\:{i}\:{hop}\:{someon}\:{Giv}\:{idea}\:{for} \\ $$$${this}\:{one}\:{thank}\:{you} \\ $$

Question Number 116271 Answers: 2 Comments: 0

∫_(−1) ^( 0) [ln(ln(1+x))]^2 dx

$$\int_{−\mathrm{1}} ^{\:\mathrm{0}} \left[{ln}\left({ln}\left(\mathrm{1}+{x}\right)\right)\right]^{\mathrm{2}} {dx} \\ $$

Question Number 116267 Answers: 2 Comments: 0

Find the equation of parabola that passes through points (1,2) ,(3,4) and tangents to the line y=−x+((25)/3)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{parabola}\:\mathrm{that} \\ $$$$\mathrm{passes}\:\mathrm{through}\:\mathrm{points}\:\left(\mathrm{1},\mathrm{2}\right)\:,\left(\mathrm{3},\mathrm{4}\right)\: \\ $$$$\mathrm{and}\:\mathrm{tangents}\:\mathrm{to}\:\mathrm{the}\:\mathrm{line}\:\mathrm{y}=−\mathrm{x}+\frac{\mathrm{25}}{\mathrm{3}} \\ $$

Question Number 116259 Answers: 1 Comments: 0

Question Number 116253 Answers: 0 Comments: 0

(1) Show that Σ_(i = 0) ^n L_i (x) = 1 (2) Show that Σ_(i = 0) ^n L_i (x). x_i ^k = x^k , k ≤ n

$$\left(\mathrm{1}\right)\:\:\:\:\mathrm{Show}\:\mathrm{that}\:\:\:\:\underset{\mathrm{i}\:\:=\:\:\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\:\mathrm{L}_{\mathrm{i}} \left(\mathrm{x}\right)\:\:\:=\:\:\:\mathrm{1} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\mathrm{Show}\:\mathrm{that}\:\:\:\:\underset{\mathrm{i}\:\:=\:\:\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\:\mathrm{L}_{\mathrm{i}} \left(\mathrm{x}\right).\:\mathrm{x}_{\mathrm{i}} ^{\mathrm{k}} \:\:\:=\:\:\:\mathrm{x}^{\mathrm{k}} ,\:\:\:\:\:\:\:\:\mathrm{k}\:\leqslant\:\mathrm{n} \\ $$

Question Number 116252 Answers: 2 Comments: 0

lim_(x→−∞) ((e^x +e^(−x) )/(e^x −e^(−x) )) = ?

$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\frac{\mathrm{e}^{\mathrm{x}} +\mathrm{e}^{−\mathrm{x}} }{\mathrm{e}^{\mathrm{x}} −\mathrm{e}^{−\mathrm{x}} }\:=\:? \\ $$

Question Number 116250 Answers: 0 Comments: 0

1)explicite U_n =∫_0 ^∞ e^(−n[x]) cos(3[x])dx 2) calculate lim_(n→+∞) U_n 3)find nsture of Σ U_n

$$\left.\mathrm{1}\right)\mathrm{explicite}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{n}\left[\mathrm{x}\right]} \mathrm{cos}\left(\mathrm{3}\left[\mathrm{x}\right]\right)\mathrm{dx} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{U}_{\mathrm{n}} \\ $$$$\left.\mathrm{3}\right)\mathrm{find}\:\mathrm{nsture}\:\mathrm{of}\:\Sigma\:\mathrm{U}_{\mathrm{n}} \\ $$

Question Number 116249 Answers: 0 Comments: 0

find ∫_0 ^1 ((arctan(x^2 +3))/(x^2 +3))dx

$$\mathrm{find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{\mathrm{arctan}\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{3}}\mathrm{dx} \\ $$

Question Number 116248 Answers: 0 Comments: 0

calculate ∫_(−∞) ^∞ ((arctan(2+x^2 ))/(x^2 −x +1))dx

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

Question Number 116247 Answers: 0 Comments: 0

find the value of I =∫_0 ^∞ ((ch(cos(2x)))/(x^2 +9))dx and J =∫_0 ^∞ ((cos(ch(2x)))/(x^2 +9))dx

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\mathrm{I}\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{ch}\left(\mathrm{cos}\left(\mathrm{2x}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{9}}\mathrm{dx}\:\mathrm{and} \\ $$$$\mathrm{J}\:=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\left(\mathrm{ch}\left(\mathrm{2x}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{9}}\mathrm{dx} \\ $$

Question Number 116245 Answers: 3 Comments: 0

calculate ∫_1 ^∞ (dx/((2x^2 −1)^5 ))

$$\mathrm{calculate}\:\:\int_{\mathrm{1}} ^{\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{2x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{5}} } \\ $$

Question Number 116239 Answers: 4 Comments: 0

a circle is tangent to x−axis , y−axis and the line 3x−4y+6=0. what its the equation?

$$\mathrm{a}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{x}−\mathrm{axis}\:,\:\mathrm{y}−\mathrm{axis} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{line}\:\mathrm{3x}−\mathrm{4y}+\mathrm{6}=\mathrm{0}. \\ $$$$\mathrm{what}\:\mathrm{its}\:\mathrm{the}\:\mathrm{equation}? \\ $$

Question Number 116238 Answers: 1 Comments: 0

How long does it take for the disintegration of (3/(10)) of an atom with radioactive constant λ ?

$$\mathrm{How}\:\mathrm{long}\:\mathrm{does}\:\mathrm{it}\:\mathrm{take}\:\mathrm{for}\:\mathrm{the}\:\mathrm{disintegration}\:\mathrm{of} \\ $$$$\frac{\mathrm{3}}{\mathrm{10}}\:\mathrm{of}\:\mathrm{an}\:\mathrm{atom}\:\mathrm{with}\:\mathrm{radioactive}\:\mathrm{constant}\:\lambda\:? \\ $$

Question Number 116237 Answers: 2 Comments: 0

∫ (√(5cos^2 x+4)) dx ?

$$\int\:\sqrt{\mathrm{5cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{4}}\:\mathrm{dx}\:? \\ $$

Question Number 116231 Answers: 1 Comments: 0

∫ sec x tan x (√(tan^2 x−3)) dx ?

$$\int\:\mathrm{sec}\:\mathrm{x}\:\mathrm{tan}\:\mathrm{x}\:\sqrt{\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}−\mathrm{3}}\:\mathrm{dx}\:? \\ $$

Question Number 116221 Answers: 3 Comments: 0

Given α,β and ϕ are the roots of x^3 −px^2 +qx−pq = 0 . Find the value of (α/β)+(β/α)+(β/ϕ)+(ϕ/β)+(α/ϕ)+(ϕ/α)=?

$$\mathrm{Given}\:\alpha,\beta\:\mathrm{and}\:\varphi\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\: \\ $$$$\mathrm{x}^{\mathrm{3}} −\mathrm{px}^{\mathrm{2}} +\mathrm{qx}−\mathrm{pq}\:=\:\mathrm{0}\:. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\alpha}{\beta}+\frac{\beta}{\alpha}+\frac{\beta}{\varphi}+\frac{\varphi}{\beta}+\frac{\alpha}{\varphi}+\frac{\varphi}{\alpha}=? \\ $$

Question Number 116216 Answers: 1 Comments: 0

∫_0 ^π ((ln (1+(1/2)cos x))/(cos x)) dx ?

$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{ln}\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{x}\right)}{\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\:? \\ $$

Question Number 116192 Answers: 2 Comments: 1

Question Number 116184 Answers: 1 Comments: 0

How many 6-digits positive integers which are formed by the digits 1 to 9 are such that each of the digits in the number appears at least twice? [For instance: 121233,122221,777777 and etc.]

$$\mathrm{How}\:\mathrm{many}\:\mathrm{6}-\mathrm{digits}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{which}\:\mathrm{are} \\ $$$$\mathrm{formed}\:\mathrm{by}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1}\:\mathrm{to}\:\mathrm{9}\:\mathrm{are}\:\mathrm{such}\:\mathrm{that}\:\mathrm{each} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{in}\:\mathrm{the}\:\mathrm{number}\:\mathrm{appears}\:\mathrm{at}\:\mathrm{least} \\ $$$$\mathrm{twice}?\:\left[\mathrm{For}\:\mathrm{instance}:\:\mathrm{121233},\mathrm{122221},\mathrm{777777}\:\mathrm{and}\:\mathrm{etc}.\right] \\ $$

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