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Question Number 61177 Answers: 0 Comments: 0

Question Number 61069 Answers: 0 Comments: 2

Question Number 61061 Answers: 1 Comments: 1

Question Number 61056 Answers: 2 Comments: 0

∫ ((x + sin(x))/(1 + cos(x))) dx

$$\int\:\frac{\mathrm{x}\:+\:\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{1}\:+\:\mathrm{cos}\left(\mathrm{x}\right)}\:\mathrm{dx} \\ $$

Question Number 61045 Answers: 2 Comments: 2

calculate I =∫_0 ^1 cos(2arctanx)dx and J =∫_0 ^1 sin(2arctanx)dx

$${calculate}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:{cos}\left(\mathrm{2}{arctanx}\right){dx} \\ $$$${and}\:{J}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:{sin}\left(\mathrm{2}{arctanx}\right){dx} \\ $$

Question Number 61042 Answers: 1 Comments: 0

Question Number 61041 Answers: 1 Comments: 1

calculate ∫_1 ^(+∞) (([2x]−[x])/x^4 ) dx

$${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{\left[\mathrm{2}{x}\right]−\left[{x}\right]}{{x}^{\mathrm{4}} }\:{dx}\: \\ $$

Question Number 61030 Answers: 0 Comments: 2

Question Number 61027 Answers: 0 Comments: 3

Question Number 61039 Answers: 0 Comments: 1

find ∫_0 ^1 arctan((2/(1+x)))dx

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

Question Number 61048 Answers: 1 Comments: 1

Question Number 61003 Answers: 3 Comments: 0

Question Number 61111 Answers: 1 Comments: 2

Please what does the 2 on the C mean. C_1 ^2 + 2 C_2 ^2 + 3 C_3 ^2 + ... + n C_n ^2 = (((2n − 1)!)/([(n − 1)!]^2 )) Does the 2 on C mean square ?? I mean: (C_1 )^2 + 2(C_2 )^2 + 3(C_3 )^2 + ... + n (C_n )^2 which is also ( ^n C_1 )^2 + 2( ^n C_2 )^2 + 3( ^n C_3 )^2 + ... + n ( ^n C_n )^2 I just want to know what the 2 on C represent . Thanks. C_1 ^2 + 2 C_2 ^2 + 3 C_3 ^2 + ... + n C_n ^2 = (((2n − 1)!)/([(n − 1)!]^2 ))

$$\mathrm{Please}\:\mathrm{what}\:\mathrm{does}\:\mathrm{the}\:\mathrm{2}\:\mathrm{on}\:\mathrm{the}\:\mathrm{C}\:\mathrm{mean}. \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathrm{C}_{\mathrm{1}} ^{\mathrm{2}} \:+\:\mathrm{2}\:\mathrm{C}_{\mathrm{2}} ^{\mathrm{2}} \:+\:\mathrm{3}\:\mathrm{C}_{\mathrm{3}} ^{\mathrm{2}} \:+\:...\:+\:\mathrm{n}\:\mathrm{C}_{\mathrm{n}} ^{\mathrm{2}} \:\:\:\:=\:\:\:\frac{\left(\mathrm{2n}\:−\:\mathrm{1}\right)!}{\left[\left(\mathrm{n}\:−\:\mathrm{1}\right)!\right]^{\mathrm{2}} } \\ $$$$\mathrm{Does}\:\mathrm{the}\:\mathrm{2}\:\mathrm{on}\:\mathrm{C}\:\mathrm{mean}\:\mathrm{square}\:?? \\ $$$$\:\:\:\:\mathrm{I}\:\mathrm{mean}:\:\:\:\:\:\:\left(\mathrm{C}_{\mathrm{1}} \right)^{\mathrm{2}} \:+\:\mathrm{2}\left(\mathrm{C}_{\mathrm{2}} \right)^{\mathrm{2}} \:+\:\mathrm{3}\left(\mathrm{C}_{\mathrm{3}} \right)^{\mathrm{2}} \:+\:...\:+\:\mathrm{n}\:\left(\mathrm{C}_{\mathrm{n}} \right)^{\mathrm{2}} \\ $$$$\mathrm{which}\:\mathrm{is}\:\mathrm{also} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left(\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{1}} \right)^{\mathrm{2}} \:+\:\mathrm{2}\left(\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{2}} \right)^{\mathrm{2}} \:+\:\mathrm{3}\left(\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{3}} \right)^{\mathrm{2}} \:+\:...\:+\:\mathrm{n}\:\left(\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{n}} \right)^{\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{I}\:\mathrm{just}\:\mathrm{want}\:\mathrm{to}\:\mathrm{know}\:\mathrm{what}\:\mathrm{the}\:\mathrm{2}\:\mathrm{on}\:\mathrm{C}\:\mathrm{represent}\:.\:\:\mathrm{Thanks}. \\ $$$$\:\:\:\:\:\:\mathrm{C}_{\mathrm{1}} ^{\mathrm{2}} \:+\:\mathrm{2}\:\mathrm{C}_{\mathrm{2}} ^{\mathrm{2}} \:+\:\mathrm{3}\:\mathrm{C}_{\mathrm{3}} ^{\mathrm{2}} \:+\:...\:+\:\mathrm{n}\:\mathrm{C}_{\mathrm{n}} ^{\mathrm{2}} \:\:\:\:=\:\:\:\frac{\left(\mathrm{2n}\:−\:\mathrm{1}\right)!}{\left[\left(\mathrm{n}\:−\:\mathrm{1}\right)!\right]^{\mathrm{2}} } \\ $$

Question Number 61202 Answers: 1 Comments: 1

Question Number 61205 Answers: 0 Comments: 4

A cubical block of ice of mass m and edge L is placed in a large tray of mass M.If the ice block melts,how far does the centre of mass of the system “ice + tray” come down ? a)((ml)/(m+M)) b)((2ml)/(m+M)) c)((ml)/(2(m+M))) d)none

$${A}\:{cubical}\:{block}\:{of}\:{ice}\:{of}\:{mass}\:{m}\:{and} \\ $$$${edge}\:{L}\:{is}\:{placed}\:{in}\:{a}\:{large}\:{tray}\:{of}\:{mass} \\ $$$${M}.{If}\:{the}\:{ice}\:{block}\:{melts},{how}\:{far}\:{does} \\ $$$${the}\:{centre}\:{of}\:{mass}\:{of}\:{the}\:{system}\:``{ice}\:+\:{tray}'' \\ $$$${come}\:{down}\:? \\ $$$$ \\ $$$$\left.{a}\left.\right)\left.\frac{{ml}}{{m}+{M}}\left.\:\:{b}\right)\frac{\mathrm{2}{ml}}{{m}+{M}}\:\:{c}\right)\frac{{ml}}{\mathrm{2}\left({m}+{M}\right)}\:\:{d}\right){none} \\ $$

Question Number 60987 Answers: 1 Comments: 1

Question Number 60984 Answers: 2 Comments: 9

(a/(a−b)) + (b/(b−c)) + (c/(c−a)) = 4 ab^2 + bc^2 + abc + ca^2 = a^2 b + b^2 c + c^2 a ((a/(a−b)))^3 + ((b/(b−c)))^3 + ((c/(c−a)))^3 = ?

$$\frac{{a}}{{a}−{b}}\:\:+\:\:\frac{{b}}{{b}−{c}}\:\:+\:\:\frac{{c}}{{c}−{a}}\:\:=\:\:\mathrm{4} \\ $$$${ab}^{\mathrm{2}} \:+\:{bc}^{\mathrm{2}} \:+\:{abc}\:+\:{ca}^{\mathrm{2}} \:\:=\:\:{a}^{\mathrm{2}} {b}\:+\:{b}^{\mathrm{2}} {c}\:+\:{c}^{\mathrm{2}} {a} \\ $$$$\left(\frac{{a}}{{a}−{b}}\right)^{\mathrm{3}} \:\:+\:\:\left(\frac{{b}}{{b}−{c}}\right)^{\mathrm{3}} \:\:+\:\:\left(\frac{{c}}{{c}−{a}}\right)^{\mathrm{3}} \:\:=\:\:? \\ $$$$ \\ $$

Question Number 60981 Answers: 2 Comments: 6

Question Number 60976 Answers: 0 Comments: 1

find Σ_(n=1) ^∞ (1/n^2 ) by use of integral ∫_0 ^(π/2) ln(2cosθ)dθ .

$${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:{by}\:{use}\:{of}\:{integral}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{2}{cos}\theta\right){d}\theta\:\:. \\ $$

Question Number 60980 Answers: 1 Comments: 2

Solve for x, y, z x(y + z) = 33 ..... (i) y(z + x) = 35 ..... (ii) z(x + y) = 14 ..... (iii)

$$\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{x},\:\mathrm{y},\:\mathrm{z} \\ $$$$\:\:\:\:\:\mathrm{x}\left(\mathrm{y}\:+\:\mathrm{z}\right)\:=\:\mathrm{33}\:\:\:\:\:\:\:\:.....\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\mathrm{y}\left(\mathrm{z}\:+\:\mathrm{x}\right)\:=\:\mathrm{35}\:\:\:\:\:\:\:\:.....\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\mathrm{z}\left(\mathrm{x}\:+\:\mathrm{y}\right)\:=\:\mathrm{14}\:\:\:\:\:\:\:\:.....\:\left(\mathrm{iii}\right) \\ $$

Question Number 60967 Answers: 0 Comments: 4

study the integral ∫_(−∞) ^(+∞) (1−cos((2/(x^2 +1))))dx

$${study}\:{the}\:{integral}\:\int_{−\infty} ^{+\infty} \left(\mathrm{1}−{cos}\left(\frac{\mathrm{2}}{{x}^{\mathrm{2}} \:+\mathrm{1}}\right)\right){dx}\: \\ $$

Question Number 60960 Answers: 0 Comments: 2

find ∫_(−∞) ^(+∞) tan((1/(1+x^2 )))dx

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

Question Number 60955 Answers: 1 Comments: 4

Question Number 60948 Answers: 0 Comments: 1

Question Number 60946 Answers: 3 Comments: 4

Find x: x^x = 2x

$$\mathrm{Find}\:\mathrm{x}:\:\:\:\:\:\:\mathrm{x}^{\mathrm{x}} \:\:=\:\:\mathrm{2x} \\ $$

Question Number 60944 Answers: 1 Comments: 1

∫(dx/((1+x^2 )^(3/2) )) solve this pls

$$\int\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$$${solve}\:{this}\:{pls} \\ $$

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