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Question Number 166191 Answers: 1 Comments: 0

∫^( (π/2)) _(−(π/2)) ((sin x)/(x^4 +x^2 +1)) dx=?

$$\:\:\:\:\:\:\:\underset{−\frac{\pi}{\mathrm{2}}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{dx}=? \\ $$

Question Number 166186 Answers: 2 Comments: 0

if sinθ = (1/2) find cosθ

$${if}\:{sin}\theta\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:{find}\:{cos}\theta \\ $$

Question Number 166182 Answers: 2 Comments: 0

calculer la primitive de ∫(t^2 /((1+t^2 )^2 ))dt

$${calculer}\:{la}\:{primitive}\:{de} \\ $$$$\int\frac{{t}^{\mathrm{2}} }{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }{dt} \\ $$

Question Number 166181 Answers: 0 Comments: 0

Question Number 166177 Answers: 1 Comments: 0

help me please A cone 9 cm high and 8 cm in base diameter is filled with ice. a) vanilla for 2/5 of the height, b) chocolate for the remaining part 1. Calculate the volume of ice it contains. 2. Calculate the volume of the vanilla ice cream and the volume of the chocolate. By what fractions must the total volume of ice be multiplied to obtain these two volumes? The different volumes will be rounded to the nearest cm³.

$$ \\ $$help me please A cone 9 cm high and 8 cm in base diameter is filled with ice. a) vanilla for 2/5 of the height, b) chocolate for the remaining part 1. Calculate the volume of ice it contains. 2. Calculate the volume of the vanilla ice cream and the volume of the chocolate. By what fractions must the total volume of ice be multiplied to obtain these two volumes? The different volumes will be rounded to the nearest cm³.

Question Number 166176 Answers: 0 Comments: 0

Question Number 166170 Answers: 2 Comments: 0

tan(a+b)=(1/(17)) , tan(a−b)=((11)/(13)) tan2a=? tan2b=?

$${tan}\left({a}+{b}\right)=\frac{\mathrm{1}}{\mathrm{17}}\:\:\:,\:\:\:{tan}\left({a}−{b}\right)=\frac{\mathrm{11}}{\mathrm{13}} \\ $$$${tan}\mathrm{2}{a}=?\:\:\:\:\:\:{tan}\mathrm{2}{b}=? \\ $$

Question Number 166169 Answers: 1 Comments: 0

sin^7 (x)+(1/(sin^3 (x)))=cos^7 (x)+(1/(cos^3 (x)))

$$\:\:\mathrm{sin}^{\mathrm{7}} \left(\mathrm{x}\right)+\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{x}\right)}=\mathrm{cos}\:^{\mathrm{7}} \left(\mathrm{x}\right)+\frac{\mathrm{1}}{\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{x}\right)} \\ $$$$ \\ $$

Question Number 166168 Answers: 0 Comments: 0

prove Σ_(r=−∞) ^∞ (1/(x + (r+(1/2))π)) = tan(x) (Σ_(r=−∞) ^∞ (1/(x + r)))(Σ_(r=−∞) ^∞ (1/(x + r))) = −(π^2 /4) ( r = odd) (r = even)

$${prove} \\ $$$$\underset{{r}=−\infty} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{x}\:+\:\left({r}+\frac{\mathrm{1}}{\mathrm{2}}\right)\pi}\:=\:{tan}\left({x}\right) \\ $$$$\left(\underset{{r}=−\infty} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{x}\:+\:{r}}\right)\left(\underset{{r}=−\infty} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{x}\:+\:{r}}\right)\:=\:−\frac{\pi^{\mathrm{2}} }{\mathrm{4}} \\ $$$$\:\:\:\:\:\left(\:{r}\:=\:{odd}\right)\:\:\:\:\:\:\:\:\left({r}\:=\:{even}\right) \\ $$

Question Number 166167 Answers: 0 Comments: 0

Question Number 166163 Answers: 0 Comments: 0

Question Number 166215 Answers: 1 Comments: 0

Question Number 166260 Answers: 1 Comments: 0

∫_0 ^(π/2) ln(sinx+cosx)dx=? −−−−−−−−−−−−by M.A

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{sinx}}+\boldsymbol{\mathrm{cosx}}\right)\boldsymbol{\mathrm{dx}}=? \\ $$$$−−−−−−−−−−−−\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{M}}.\boldsymbol{\mathrm{A}} \\ $$

Question Number 166160 Answers: 3 Comments: 0

Σ_(n=1) ^∞ Σ_(m=1) ^∞ (1/(m^2 n+mn^2 +2mn))=?

$$\:\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{\mathrm{m}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{m}^{\mathrm{2}} \mathrm{n}+\mathrm{mn}^{\mathrm{2}} +\mathrm{2mn}}=? \\ $$

Question Number 166143 Answers: 1 Comments: 0

Question Number 166141 Answers: 2 Comments: 0

∫_0 ^x (t^2 /( (√(a+2t^2 ))))dt

$$\int_{\mathrm{0}} ^{\boldsymbol{\mathrm{x}}} \frac{\boldsymbol{\mathrm{t}}^{\mathrm{2}} }{\:\sqrt{\boldsymbol{\mathrm{a}}+\mathrm{2}\boldsymbol{\mathrm{t}}^{\mathrm{2}} }}\boldsymbol{\mathrm{dt}}\: \\ $$

Question Number 166137 Answers: 2 Comments: 0

Question Number 166135 Answers: 1 Comments: 1

find the domain of f(x) = (1/([x]−1))

$${find}\:{the}\:{domain}\:{of}\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\left[{x}\right]−\mathrm{1}} \\ $$

Question Number 166134 Answers: 1 Comments: 0

Question Number 166127 Answers: 0 Comments: 0

Question Number 166125 Answers: 0 Comments: 0

Question Number 166120 Answers: 1 Comments: 2

Question Number 166113 Answers: 2 Comments: 2

prove that 1!=1

$${prove}\:{that}\:\mathrm{1}!=\mathrm{1} \\ $$

Question Number 166112 Answers: 1 Comments: 1

prove that 0!=1

$${prove}\:{that}\:\mathrm{0}!=\mathrm{1} \\ $$

Question Number 166111 Answers: 1 Comments: 0

Question Number 166110 Answers: 1 Comments: 0

Prove that ((( n)),(( 0)) )^2 + ((( n)),(( 1)) )^2 + ((( n)),(( 2)) )^2 + …+ ((( n)),(( n)) )^2 = ((( 2n)),(( n)) )

$$\mathrm{Prove}\:\:\mathrm{that} \\ $$$$\:\begin{pmatrix}{\:{n}}\\{\:\mathrm{0}}\end{pmatrix}^{\mathrm{2}} \:+\:\begin{pmatrix}{\:{n}}\\{\:\mathrm{1}}\end{pmatrix}^{\mathrm{2}} \:+\:\begin{pmatrix}{\:{n}}\\{\:\mathrm{2}}\end{pmatrix}^{\mathrm{2}} \:+\:\ldots+\:\begin{pmatrix}{\:{n}}\\{\:{n}}\end{pmatrix}^{\mathrm{2}} \:\:=\:\:\begin{pmatrix}{\:\mathrm{2}{n}}\\{\:\:{n}}\end{pmatrix} \\ $$

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