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Question Number 206890    Answers: 0   Comments: 1

can some one find the exact value of Σ_(n=0) ^∞ (1/((n!)^2 ))

$${can}\:{some}\:{one}\:{find}\:{the}\:{exact}\:{value}\:{of} \\ $$$$\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{\left({n}!\right)^{\mathrm{2}} } \\ $$

Question Number 206858    Answers: 2   Comments: 0

prove that H_n =∫_0 ^1 ((t^n −1)/(t−1))dt

$$\mathrm{prove}\:\mathrm{that} \\ $$$${H}_{{n}} =\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{t}^{{n}} −\mathrm{1}}{{t}−\mathrm{1}}{dt} \\ $$

Question Number 206830    Answers: 0   Comments: 0

c = (√((∫_a_0 ^a_1 (√(1+[f′(x)]^2 ))dx)^2 +(∫_b_0 ^b_1 (√(1+[f′(x)]^2 ))dx)^2 )) c = (√(L_1 ^2 +L_2 ^2 ))

$${c}\:=\:\sqrt{\left(\int_{{a}_{\mathrm{0}} } ^{{a}_{\mathrm{1}} } \sqrt{\mathrm{1}+\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{dx}\right)^{\mathrm{2}} +\left(\int_{{b}_{\mathrm{0}} } ^{{b}_{\mathrm{1}} } \sqrt{\mathrm{1}+\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{dx}\right)^{\mathrm{2}} } \\ $$$${c}\:=\:\sqrt{{L}_{\mathrm{1}} ^{\mathrm{2}} +{L}_{\mathrm{2}} ^{\mathrm{2}} } \\ $$

Question Number 206829    Answers: 0   Comments: 1

∮(x/(x+2))dx^2 is wrong?

$$\:\:\:\:\:\oint\frac{{x}}{{x}+\mathrm{2}}{dx}^{\mathrm{2}} \:\:\:\:{is}\:{wrong}? \\ $$

Question Number 206789    Answers: 1   Comments: 0

Question Number 206754    Answers: 1   Comments: 0

find ∫_0 ^1 (√(1−(√x)))ln^2 (x)dx

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

Question Number 206721    Answers: 4   Comments: 0

∫((xdx)/(x+4))=? please

$$\int\frac{{xdx}}{{x}+\mathrm{4}}=?\:\:\:\:\:\:\:{please} \\ $$

Question Number 206791    Answers: 0   Comments: 3

∫_0 ^1 (√(1−(√x))).ln^2 x dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−\sqrt{\mathrm{x}}}.\mathrm{ln}^{\mathrm{2}} \mathrm{x}\:\mathrm{dx} \\ $$

Question Number 206645    Answers: 1   Comments: 5

Let f(x)=x(x−10) and let A be the region enclosed within the following points (2,7),(8,7),(2,4),(8,4) what is the average arc length of a∙f(x) inside A,a∈R^−

$$\mathrm{Let}\:{f}\left({x}\right)={x}\left({x}−\mathrm{10}\right) \\ $$$$\mathrm{and}\:\mathrm{let}\:\mathrm{A}\:\mathrm{be}\:\mathrm{the}\:\mathrm{region}\:\mathrm{enclosed}\:\mathrm{within} \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{points} \\ $$$$\left(\mathrm{2},\mathrm{7}\right),\left(\mathrm{8},\mathrm{7}\right),\left(\mathrm{2},\mathrm{4}\right),\left(\mathrm{8},\mathrm{4}\right) \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{average}\:\mathrm{arc}\:\mathrm{length}\:\mathrm{of}\:\mathrm{a}\centerdot{f}\left({x}\right) \\ $$$$\mathrm{inside}\:\mathrm{A},{a}\in\mathbb{R}^{−} \\ $$

Question Number 206642    Answers: 0   Comments: 0

Question Number 206639    Answers: 0   Comments: 1

Question Number 206592    Answers: 2   Comments: 0

Question Number 206579    Answers: 1   Comments: 0

Evaluate : ∫_0 ^1 ((ln (1+x^2 ))/(1+x))d(x).

$$\mathrm{Evaluate}\::\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{\mathrm{ln}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}}{d}\left({x}\right). \\ $$

Question Number 206568    Answers: 1   Comments: 0

Question Number 206558    Answers: 1   Comments: 0

Question Number 206557    Answers: 1   Comments: 0

Question Number 206549    Answers: 2   Comments: 2

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

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

Question Number 206543    Answers: 1   Comments: 0

Question Number 206542    Answers: 1   Comments: 0

Question Number 206541    Answers: 1   Comments: 0

Question Number 206537    Answers: 1   Comments: 0

∫((x^4 −1)/(x^2 (√(x^4 +x^2 +1))))dx

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

Question Number 206536    Answers: 1   Comments: 1

∫ ((2^x sin ((√(4−2^(x+2) )) ))/( (√(1−2^x )) cos ((√(1−2^x )) ) )) dx =?

$$\:\:\: \int\:\frac{\mathrm{2}^{{x}} \:\mathrm{sin}\:\left(\sqrt{\mathrm{4}−\mathrm{2}^{{x}+\mathrm{2}} }\:\right)}{\:\sqrt{\mathrm{1}−\mathrm{2}^{{x}} }\:\mathrm{cos}\:\left(\sqrt{\mathrm{1}−\mathrm{2}^{{x}} }\:\right)\:}\:{dx}\:=? \\ $$

Question Number 206490    Answers: 1   Comments: 0

Resuelve la siguiente integral ∫ ((cos (t))/( ((sin^7 (t)∙cos^5 (t)))^(1/4) )) dt

$${Resuelve}\:{la}\:{siguiente}\:{integral} \\ $$$$\int\:\frac{\mathrm{cos}\:\left({t}\right)}{\:\sqrt[{\mathrm{4}}]{\mathrm{sin}^{\mathrm{7}} \left({t}\right)\centerdot\mathrm{cos}^{\mathrm{5}} \left({t}\right)}}\:{dt} \\ $$

Question Number 206489    Answers: 1   Comments: 0

Resuelve la siguiente integral ∫ ((sin (t))/( ((sin^7 (t)∙cos^5 (t)))^(1/4) )) dt

$${Resuelve}\:{la}\:{siguiente}\:{integral} \\ $$$$\int\:\frac{\mathrm{sin}\:\left({t}\right)}{\:\sqrt[{\mathrm{4}}]{\mathrm{sin}^{\mathrm{7}} \left({t}\right)\centerdot\mathrm{cos}^{\mathrm{5}} \left({t}\right)}}\:{dt} \\ $$

Question Number 206338    Answers: 1   Comments: 0

Question Number 206248    Answers: 1   Comments: 0

∫(1/( (√((1−t)(2−t)))))dt=...?

$$\int\frac{\mathrm{1}}{\:\sqrt{\left(\mathrm{1}−{t}\right)\left(\mathrm{2}−{t}\right)}}{dt}=...? \\ $$

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