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Question Number 145780 Answers: 1 Comments: 0

find the volume of the solid generated by the region bounded by y=(√x) , 0≤x≤1 and X−axis

$${find}\:{the}\:{volume}\:{of}\:{the}\:{solid}\: \\ $$$${generated}\:{by}\:{the}\:{region}\:{bounded}\:{by} \\ $$$${y}=\sqrt{{x}}\:,\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\:{X}−{axis} \\ $$

Question Number 145779 Answers: 1 Comments: 0

lim_(x→0) ∫_0 ^1 (e^t +e^(−t) −2)(dt/(1−cosx))

$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\int_{\mathrm{0}} ^{\mathrm{1}} \left({e}^{{t}} +{e}^{−{t}} −\mathrm{2}\right)\frac{{dt}}{\mathrm{1}−{cosx}} \\ $$

Question Number 145777 Answers: 2 Comments: 0

∫(1/( (√(1−9x^2 ))))dx

$$\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\mathrm{9}{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 145776 Answers: 2 Comments: 0

∫_0 ^(π/2) e^x cosxdx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {e}^{{x}} {cosxdx} \\ $$

Question Number 145775 Answers: 2 Comments: 0

∫((2x+1)/( (√(x^2 +4x+5))))dx

$$\int\frac{\mathrm{2}{x}+\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{5}}}{dx} \\ $$

Question Number 145772 Answers: 0 Comments: 0

a;b;c>0 ; a^2 +b^2 +c^2 =2 prove: (a^6 +b^6 +c^6 )^3 ≥ (a^5 +b^5 +c^5 )^4

$${a};{b};{c}>\mathrm{0}\:;\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{2}\:{prove}: \\ $$$$\left({a}^{\mathrm{6}} +{b}^{\mathrm{6}} +{c}^{\mathrm{6}} \right)^{\mathrm{3}} \:\geqslant\:\left({a}^{\mathrm{5}} +{b}^{\mathrm{5}} +{c}^{\mathrm{5}} \right)^{\mathrm{4}} \\ $$

Question Number 145774 Answers: 1 Comments: 0

find the area bounded by y=2x, y=(x/2) and?xy=2

$${find}\:{the}\:{area}\:{bounded}\:{by}\:{y}=\mathrm{2}{x},\:{y}=\frac{{x}}{\mathrm{2}}\:{and}?{xy}=\mathrm{2} \\ $$

Question Number 145773 Answers: 1 Comments: 0

Question Number 145769 Answers: 1 Comments: 1

find x if 2^x +2^(3x) =16

$${find}\:{x}\:{if}\:\:\mathrm{2}^{{x}} +\mathrm{2}^{\mathrm{3}{x}} =\mathrm{16} \\ $$

Question Number 145768 Answers: 0 Comments: 0

x;y;z;t∈Z^+ { ((xy + zt = 38)),((xz + yt = 34)),((xt + yz = 43)) :} ⇒ x+y+z+t=?

$${x};{y};{z};{t}\in\mathbb{Z}^{+} \\ $$$$\begin{cases}{{xy}\:+\:{zt}\:=\:\mathrm{38}}\\{{xz}\:+\:{yt}\:=\:\mathrm{34}}\\{{xt}\:+\:{yz}\:=\:\mathrm{43}}\end{cases}\:\:\Rightarrow\:{x}+{y}+{z}+{t}=? \\ $$

Question Number 145766 Answers: 0 Comments: 0

Question Number 145760 Answers: 0 Comments: 0

Question Number 145759 Answers: 1 Comments: 2

Question Number 145756 Answers: 2 Comments: 0

Question Number 145809 Answers: 1 Comments: 0

prove 1+2+3+.....=−(1/(12))

$$\mathrm{prove}\:\mathrm{1}+\mathrm{2}+\mathrm{3}+.....=−\frac{\mathrm{1}}{\mathrm{12}} \\ $$

Question Number 145751 Answers: 1 Comments: 4

Question Number 145750 Answers: 0 Comments: 0

find Σ_(n=0) ^∞ (((−1)^n )/((2n+1)^3 (n+3)^2 ))

$$\mathrm{find}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\left(\mathrm{2n}+\mathrm{1}\right)^{\mathrm{3}} \left(\mathrm{n}+\mathrm{3}\right)^{\mathrm{2}} } \\ $$

Question Number 145749 Answers: 1 Comments: 0

g(x)=log(tan(x)) developp g at fourier serie

$$\mathrm{g}\left(\mathrm{x}\right)=\mathrm{log}\left(\mathrm{tan}\left(\mathrm{x}\right)\right)\:\mathrm{developp}\:\mathrm{g}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 145748 Answers: 1 Comments: 0

f(x)=arctan(2sinx) developp f at fourier serie

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{arctan}\left(\mathrm{2sinx}\right) \\ $$$$\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 145763 Answers: 1 Comments: 0

if z=(((3+i sin θ)/(4−i cos θ)))is purely real and (Π/2)<θ<Π then find arg(sin θ +i cos θ)?

$${if}\:{z}=\left(\frac{\mathrm{3}+{i}\:\mathrm{sin}\:\theta}{\mathrm{4}−{i}\:\mathrm{cos}\:\theta}\right){is}\:{purely}\:{real}\:{and}\: \\ $$$$\frac{\Pi}{\mathrm{2}}<\theta<\Pi\:{then}\:{find}\:{arg}\left(\mathrm{sin}\:\theta\:+{i}\:\mathrm{cos}\:\theta\right)? \\ $$

Question Number 145746 Answers: 0 Comments: 0

find ∫_0 ^1 log(x)log(1−x)log(1−x^2 )dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{log}\left(\mathrm{x}\right)\mathrm{log}\left(\mathrm{1}−\mathrm{x}\right)\mathrm{log}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx} \\ $$

Question Number 145745 Answers: 1 Comments: 0

calculate ∫_0 ^∞ ((cos(2x))/((x^2 +1)^2 (x^2 +4)))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}\right)}\mathrm{dx} \\ $$

Question Number 145755 Answers: 0 Comments: 0

Let a,b,c > 0 and abc = 1. Prove that ((8(a^2 +1)(b^2 +1)(c^2 +1))/((a+1)(b+1)(c+1))) ≤ (a+b)(b+c)(c+a)

$$\mathrm{Let}\:{a},{b},{c}\:>\:\mathrm{0}\:\mathrm{and}\:{abc}\:=\:\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that}\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{8}\left({a}^{\mathrm{2}} +\mathrm{1}\right)\left({b}^{\mathrm{2}} +\mathrm{1}\right)\left({c}^{\mathrm{2}} +\mathrm{1}\right)}{\left({a}+\mathrm{1}\right)\left({b}+\mathrm{1}\right)\left({c}+\mathrm{1}\right)}\:\leqslant\:\left({a}+{b}\right)\left({b}+{c}\right)\left({c}+{a}\right) \\ $$

Question Number 145729 Answers: 0 Comments: 0

Dl of f(x)=(√(x(1+x)))e^(3/(2x)) ..

$$\mathrm{Dl}\:\:\:\mathrm{of}\:\:\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}\left(\mathrm{1}+\mathrm{x}\right)}\mathrm{e}^{\frac{\mathrm{3}}{\mathrm{2x}}} .. \\ $$

Question Number 145724 Answers: 5 Comments: 1

Question Number 145723 Answers: 1 Comments: 0

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