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IntegrationQuestion and Answers: Page 164

Question Number 100513 Answers: 0 Comments: 0

findA_(nm) =∫_0 ^∞ e^(−nx) ∣sin(px)∣ dx with n and p integr natural ≥1

$$\mathrm{findA}_{\mathrm{nm}} \:=\int_{\mathrm{0}} ^{\infty} \:\:\mathrm{e}^{−\mathrm{nx}} \:\mid\mathrm{sin}\left(\mathrm{px}\right)\mid\:\mathrm{dx}\:\:\mathrm{with}\:\:\mathrm{n}\:\mathrm{and}\:\mathrm{p}\:\mathrm{integr}\:\mathrm{natural}\:\geqslant\mathrm{1} \\ $$

Question Number 100512 Answers: 0 Comments: 0

calculate ∫_(−∞) ^(+∞) (x^n /((x^2 +x+1)^n )) dx with n integr and n≥2

$$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{x}^{\mathrm{n}} }{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}\right)^{\mathrm{n}} }\:\mathrm{dx}\:\:\mathrm{with}\:\mathrm{n}\:\mathrm{integr}\:\mathrm{and}\:\mathrm{n}\geqslant\mathrm{2} \\ $$

Question Number 100511 Answers: 1 Comments: 0

calculate ∫_(−∞) ^∞ ((arctan(cosx +sinx))/(x^2 +4)) dx

$$\mathrm{calculate}\:\:\int_{−\infty} ^{\infty} \:\:\frac{\mathrm{arctan}\left(\mathrm{cosx}\:+\mathrm{sinx}\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}}\:\mathrm{dx} \\ $$

Question Number 100468 Answers: 3 Comments: 0

Σ_(n=1) ^∞ (n/((2n+1)!)) help me pls

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}}{\left(\mathrm{2}{n}+\mathrm{1}\right)!} \\ $$$${help}\:{me}\:{pls} \\ $$

Question Number 100450 Answers: 1 Comments: 0

Question Number 100438 Answers: 0 Comments: 5

∫_0 ^1 ∫_0 ^x x^2 y^(xy) dydx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{{x}} {x}^{\mathrm{2}} {y}^{{xy}} {dydx} \\ $$

Question Number 100362 Answers: 3 Comments: 0

∫_0 ^1 ∫_0 ^1 e^(2x+y) dydx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} {e}^{\mathrm{2}{x}+{y}} {dydx} \\ $$

Question Number 100368 Answers: 1 Comments: 0

lim_(n→∞) ∫_(−∞) ^∞ cos (x^n ) dx =? where n=2k, k∈N, k≠0

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\int_{−\infty} ^{\infty} \mathrm{cos}\:\left({x}^{{n}} \right)\:{dx}\:=? \\ $$$${where}\:{n}=\mathrm{2}{k},\:{k}\in\mathbb{N},\:{k}\neq\mathrm{0} \\ $$

Question Number 100216 Answers: 1 Comments: 2

if I = ∫_0 ^(π/2) ((sin x)/(sin x + cos x))dx = ∫_0 ^(π/2) ((cos x)/(sin x +cos x))dx then I = ??

$$\mathrm{if}\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x}}{dx}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}\:+\mathrm{cos}\:{x}}{dx}\: \\ $$$$\mathrm{then}\:{I}\:=\:?? \\ $$

Question Number 100215 Answers: 2 Comments: 1

evaluate lim_(n→∞) ∫_1 ^e x^n ln x dx

$$\mathrm{evaluate}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{1}} ^{{e}} {x}^{{n}} \mathrm{ln}\:{x}\:{dx}\: \\ $$

Question Number 100207 Answers: 0 Comments: 2

Given an even fuction f(x) such that ∫_(−a) ^a f(x)dx = (√a) ∀a ≥0 find ∫_3 ^4 f(x) dx

$$\mathrm{Given}\:\mathrm{an}\:\mathrm{even}\:\mathrm{fuction}\:{f}\left({x}\right)\:\mathrm{such}\:\mathrm{that}\:\overset{{a}} {\int}_{−{a}} \:{f}\left({x}\right){dx}\:=\:\sqrt{{a}}\:\forall{a}\:\geqslant\mathrm{0} \\ $$$$\mathrm{find}\:\int_{\mathrm{3}} ^{\mathrm{4}} {f}\left({x}\right)\:{dx} \\ $$$$ \\ $$

Question Number 100191 Answers: 1 Comments: 1

∫ x^2 e^x dx ?

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

Question Number 100190 Answers: 0 Comments: 0

∫_0 ^1 ((x^x /((1−x)^(1−x) ))−(((1−x)^(1−x) )/x^x ))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{{x}^{{x}} }{\left(\mathrm{1}−{x}\right)^{\mathrm{1}−{x}} }−\frac{\left(\mathrm{1}−{x}\right)^{\mathrm{1}−{x}} }{{x}^{{x}} }\right){dx} \\ $$

Question Number 100189 Answers: 1 Comments: 0

∫tan^i xdx

$$\int{tan}^{{i}} {xdx} \\ $$

Question Number 100114 Answers: 1 Comments: 0

Question Number 100089 Answers: 0 Comments: 0

calculate A_n =∫_0 ^(π/2) ((sin^n (x))/(sin(nx)))dx

$$\:\mathrm{calculate}\:\mathrm{A}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{sin}^{\mathrm{n}} \left(\mathrm{x}\right)}{\mathrm{sin}\left(\mathrm{nx}\right)}\mathrm{dx}\: \\ $$

Question Number 100088 Answers: 1 Comments: 1

calculate ∫ ((cosx)/(cos(3x)))dx

$$\mathrm{calculate}\:\int\:\frac{\mathrm{cosx}}{\mathrm{cos}\left(\mathrm{3x}\right)}\mathrm{dx} \\ $$

Question Number 100054 Answers: 1 Comments: 0

I_(n,m) =∫_0 ^1 ∫_0 ^1 (((ln(x))^n (ln(y))^m )/(1−xy))dx dy

$${I}_{{n},{m}} =\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left({ln}\left({x}\right)\right)^{{n}} \left({ln}\left({y}\right)\right)^{{m}} }{\mathrm{1}−{xy}}{dx}\:{dy} \\ $$

Question Number 100047 Answers: 2 Comments: 0

∫_0 ^1 e^(−x^2 ) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{dx} \\ $$

Question Number 100026 Answers: 1 Comments: 0

∫_0 ^(π/2) e^(−sec^2 θ) dθ

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{e}^{−\mathrm{sec}^{\mathrm{2}} \theta} \mathrm{d}\theta \\ $$

Question Number 99831 Answers: 0 Comments: 0

solve the ds { ((x^′ +2y^′ =sint)),((3x^′ +y^′ =te^t )) :}

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{ds}\:\:\:\begin{cases}{\mathrm{x}^{'} \:+\mathrm{2y}^{'} \:=\mathrm{sint}}\\{\mathrm{3x}^{'} +\mathrm{y}^{'} \:=\mathrm{te}^{\mathrm{t}} }\end{cases} \\ $$

Question Number 99824 Answers: 1 Comments: 0

calculate ∫_0 ^1 xe^(−x^2 ) arctan((2/x))dx

$$\mathrm{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{xe}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{arctan}\left(\frac{\mathrm{2}}{\mathrm{x}}\right)\mathrm{dx} \\ $$

Question Number 99820 Answers: 0 Comments: 0

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

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

Question Number 99818 Answers: 2 Comments: 0

∫_0 ^1 ln(1+(1/(n^2 x^2 )))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} }\right)\mathrm{dx} \\ $$

Question Number 99779 Answers: 1 Comments: 2

Question Number 99707 Answers: 4 Comments: 1

∫_(−∞) ^∞ e^(−x^2 ) dx=?

$$\int_{−\infty} ^{\infty} \mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{dx}=? \\ $$

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