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Question Number 66540 Answers: 0 Comments: 0

graph the function r^2 =cos(2θ) and find the area?

$${graph}\:{the}\:{function}\:{r}^{\mathrm{2}} ={cos}\left(\mathrm{2}\theta\right)\:{and}\:{find}\:{the}\:{area}? \\ $$

Question Number 66536 Answers: 0 Comments: 0

∫ln^(10) (x) sin^7 (x) dx

$$\int{ln}^{\mathrm{10}} \left({x}\right)\:{sin}^{\mathrm{7}} \left({x}\right)\:{dx} \\ $$

Question Number 66520 Answers: 0 Comments: 1

find the length r=2/1−cosθ if θ between pi/2 to pi

$${find}\:{the}\:{length}\:{r}=\mathrm{2}/\mathrm{1}−{cos}\theta\:\:\:\:\:\:\:\:\:{if}\:\theta\:{between}\:{pi}/\mathrm{2}\:{to}\:{pi} \\ $$

Question Number 66517 Answers: 1 Comments: 1

find the area cos(2θ)

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

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 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 66476 Answers: 0 Comments: 1

Question Number 66474 Answers: 0 Comments: 2

∫e^x^2 dx=?

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

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 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 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 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 66405 Answers: 0 Comments: 0

Question Number 66404 Answers: 0 Comments: 3

Question Number 66403 Answers: 0 Comments: 0

Question Number 66401 Answers: 0 Comments: 0

Question Number 66351 Answers: 0 Comments: 1

let I_n =∫_0 ^∞ (e^(nt) /((1+e^t )^(n+1) ))dt (n from N^★ ) )prove the existence of I_n 2)find lim_(n→+∞) I_n

$${let}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{{nt}} }{\left(\mathrm{1}+{e}^{{t}} \right)^{{n}+\mathrm{1}} }{dt}\:\:\:\:\:\left({n}\:{from}\:{N}^{\bigstar} \right) \\ $$$$\left.\right){prove}\:{the}\:{existence}\:{of}\:{I}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:{I}_{{n}} \\ $$

Question Number 66350 Answers: 0 Comments: 1

study the convergence of ∫_0 ^∞ (1−(√(x^n /(2+x^n ))))dx n∈N

$${study}\:{the}\:{convergence}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\left(\mathrm{1}−\sqrt{\frac{{x}^{{n}} }{\mathrm{2}+{x}^{{n}} }}\right){dx}\:\:\:\:{n}\in{N} \\ $$

Question Number 66349 Answers: 0 Comments: 1

study the convergence of ∫_1 ^(+∞) ((arctan(x−1))/((x^2 −1)^(4/3) ))dx

$${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{arctan}\left({x}−\mathrm{1}\right)}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} }{dx} \\ $$

Question Number 66348 Answers: 0 Comments: 0

find nature of ∫_0 ^1 (dx/(e^x −cosx))

$${find}\:{nature}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{{e}^{{x}} −{cosx}} \\ $$

Question Number 66347 Answers: 0 Comments: 0

let I_n =∫_0 ^1 ((x^(2n+1) ln(x))/(x^2 −1))dx 1) prove the existence of I_n 2)calculate I_(n+1) −I_n 3)prove thst x∈]0,1[ ⇒0<((xlnx)/(x^2 −1))<(1/2) 4) find lim_(n→+∞) I_n

$${let}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} {ln}\left({x}\right)}{{x}^{\mathrm{2}} −\mathrm{1}}{dx} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{the}\:{existence}\:{of}\:{I}_{{n}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{I}_{{n}+\mathrm{1}} −{I}_{{n}} \\ $$$$\left.\mathrm{3}\left.\right){prove}\:{thst}\:{x}\in\right]\mathrm{0},\mathrm{1}\left[\:\Rightarrow\mathrm{0}<\frac{{xlnx}}{{x}^{\mathrm{2}} −\mathrm{1}}<\frac{\mathrm{1}}{\mathrm{2}}\right. \\ $$$$\left.\mathrm{4}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{I}_{{n}} \\ $$

Question Number 66346 Answers: 0 Comments: 2

find ∫_0 ^∞ (t^7 /(t^(16) +1))dt

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{t}^{\mathrm{7}} }{{t}^{\mathrm{16}} \:+\mathrm{1}}{dt} \\ $$

Question Number 66345 Answers: 0 Comments: 1

find the value of ∫_(−∞) ^(+∞) (dt/((t^2 −2t +2)^(3/2) ))

$${find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{t}\:+\mathrm{2}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$

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