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Question Number 66518 Answers: 0 Comments: 2

Question Number 66517 Answers: 1 Comments: 1

find the area cos(2θ)

$${find}\:{the}\:{area}\:{cos}\left(\mathrm{2}\theta\right) \\ $$

Question Number 66513 Answers: 1 Comments: 4

when finding ∫_0 ^2 (2x +4)^5 dx must we change limits?

$${when}\:{finding}\:\:\int_{\mathrm{0}} ^{\mathrm{2}} \left(\mathrm{2}{x}\:+\mathrm{4}\right)^{\mathrm{5}} {dx}\: \\ $$$${must}\:{we}\:{change}\:{limits}? \\ $$

Question Number 66508 Answers: 0 Comments: 3

Question Number 66502 Answers: 1 Comments: 0

find the area about cos(2θ)

$${find}\:{the}\:{area}\:{about}\:{cos}\left(\mathrm{2}\theta\right) \\ $$

Question Number 66498 Answers: 1 Comments: 3

Question Number 66497 Answers: 1 Comments: 0

Question Number 66489 Answers: 3 Comments: 0

Question Number 66483 Answers: 0 Comments: 4

calculate Σ_(k=2) ^∞ (((−1)^k )/k) ζ(k) if ζ(s)=Σ_(n=1) ^∞ (1/n^s )

$$\:{calculate}\:\:\:\:\underset{{k}=\mathrm{2}} {\overset{\infty} {\sum}}\:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}}\:\zeta\left({k}\right)\:\:\:\:\:\:\:{if}\:\:\:\:\zeta\left({s}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{1}}{{n}^{{s}} }\: \\ $$

Question Number 66478 Answers: 0 Comments: 2

lim_(x→2) [((log_x (2)−1)/(log_2 ((1/x))+1))]=?

$$\: \\ $$$$\:\underset{\boldsymbol{{x}}\rightarrow\mathrm{2}} {\boldsymbol{{lim}}}\left[\frac{\boldsymbol{{log}}_{\boldsymbol{{x}}} \left(\mathrm{2}\right)−\mathrm{1}}{\boldsymbol{{log}}_{\mathrm{2}} \left(\frac{\mathrm{1}}{\boldsymbol{{x}}}\right)+\mathrm{1}}\right]=? \\ $$$$\: \\ $$

Question Number 66476 Answers: 0 Comments: 1

Question Number 66474 Answers: 0 Comments: 2

∫e^x^2 dx=?

$$\int{e}^{{x}^{\mathrm{2}} } {dx}=? \\ $$

Question Number 66472 Answers: 1 Comments: 0

{ (((x)^(1/(√6)) +(y)^(1/(√5)) =11)),((((y)^(1/(√5)) /(x)^(1/(√6)) )=1(1/5))) :} Qual e^ o par ordenado na forma a^(√p) e b^(√q) que satisfaz o sistema como possivel e determinado?

Question Number 66470 Answers: 0 Comments: 5

calculate ∫_0 ^∞ (dx/((x^n +8)^3 )) withn>1

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{dx}}{\left({x}^{{n}} \:+\mathrm{8}\right)^{\mathrm{3}} }\:\:{withn}>\mathrm{1} \\ $$

Question Number 66469 Answers: 0 Comments: 1

Question Number 66468 Answers: 0 Comments: 1

calculate I_n = ∫_0 ^∞ (dx/((x^n +3)^2 )) with n>1

$${calculate}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left({x}^{{n}} \:+\mathrm{3}\right)^{\mathrm{2}} }\:\:{with}\:{n}>\mathrm{1} \\ $$

Question Number 66467 Answers: 0 Comments: 1

calculate A_n =∫_0 ^∞ (dx/((n+x^n )^2 )) with n>1

$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({n}+{x}^{{n}} \right)^{\mathrm{2}} }\:\:\:{with}\:{n}>\mathrm{1} \\ $$

Question Number 66466 Answers: 0 Comments: 1

find f(a,b) =∫_0 ^∞ ((cos(ax)cos(bx))/((x^2 +a^2 )(x^2 +b^2 )))dx with a>0 and b>0 2)calculate ∫_0 ^∞ ((cos(x)cos(2x))/((x^2 +1)(x^2 +4)))dx

$${find}\:\:{f}\left({a},{b}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left({ax}\right){cos}\left({bx}\right)}{\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \right)}{dx}\:\:{with}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({x}\right){cos}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{4}\right)}{dx} \\ $$

Question Number 66465 Answers: 0 Comments: 1

calculate ∫_0 ^∞ (dx/((x^2 +2i)( x^2 +4j))) with i=e^((iπ)/2) and j=e^(i((2π)/3))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{2}{i}\right)\left(\:{x}^{\mathrm{2}} \:+\mathrm{4}{j}\right)}\:\:\:{with}\:{i}={e}^{\frac{{i}\pi}{\mathrm{2}}} \:{and}\:{j}={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \\ $$

Question Number 66464 Answers: 0 Comments: 1

calculate ∫_0 ^∞ (dx/((x^2 +3)(x^2 +8)^2 ))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)\left({x}^{\mathrm{2}} +\mathrm{8}\right)^{\mathrm{2}} } \\ $$

Question Number 66681 Answers: 0 Comments: 2

Question Number 66462 Answers: 0 Comments: 1

1)simplify S_n (x)=Σ_(k=0) ^n C_n ^k cos^k (x)cos(kx) 2)find the value of A_n =Σ_(k=0) ^n C_n ^k cos^k ((π/n))cos(((kπ)/n))

$$\left.\mathrm{1}\right){simplify}\:{S}_{{n}} \left({x}\right)=\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{cos}^{{k}} \left({x}\right){cos}\left({kx}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{cos}^{{k}} \left(\frac{\pi}{{n}}\right){cos}\left(\frac{{k}\pi}{{n}}\right) \\ $$

Question Number 66461 Answers: 0 Comments: 0

x(n)=3n^2 −2n+7 find even and odd component

$${x}\left({n}\right)=\mathrm{3}{n}^{\mathrm{2}} −\mathrm{2}{n}+\mathrm{7} \\ $$$${find}\:{even}\:{and}\:{odd}\:{component} \\ $$

Question Number 66459 Answers: 0 Comments: 1

1) calculate by residus method ∫_0 ^∞ (dx/((1+x^2 )^3 )) 2) find the value of ∫_0 ^1 ((1+x^4 )/((1+x^2 )^3 ))dx

$$\left.\mathrm{1}\right)\:{calculate}\:{by}\:{residus}\:{method}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} } \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{1}+{x}^{\mathrm{4}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} }{dx} \\ $$

Question Number 66446 Answers: 0 Comments: 1

Find ∫_1 ^∞ ((1/(E(x))) −(1/x))dx

$$\:\:{Find}\:\:\:\:\int_{\mathrm{1}} ^{\infty} \:\left(\frac{\mathrm{1}}{{E}\left({x}\right)}\:−\frac{\mathrm{1}}{{x}}\right){dx} \\ $$

Question Number 66444 Answers: 0 Comments: 1

calculate lim_(x→0) (x!)^(1/x) if x!=Π(x)=∫_0 ^∞ t^x e^(−t) dt

$$\:{calculate}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\left({x}!\right)^{\frac{\mathrm{1}}{{x}}} \:\:\:\:\:\:\:{if}\:\:\:\:\:{x}!=\Pi\left({x}\right)=\int_{\mathrm{0}} ^{\infty} {t}^{{x}} \:{e}^{−{t}} {dt} \\ $$

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