Mathematics: Find the arc length of the curve: y = 1/3(x^2+2)^(3/2). from x=0 to x=3

Find the arc length of the curve: y = 1/3(x^2+2)^(3/2).

Ответ:

Courtneymorris19

14.01.2022

$y=\dfrac13(x^2+2)^{3/2}\implies y'=x(x^2+2)^{1/2}\implies (y')^2=x^4+2x^2$

The arc length is given by

$\displaystyle\int_{x=0}^{x=3}\sqrt{1+(y')^2}\,\mathrm dx=\int_0^3\sqrt{x^4+2x^2+1}\,\mathrm dx$
$=\displaystyle\int_0^3\sqrt{(x^2+1)^2}\,\mathrm dx$
$=\displaystyle\int_0^3(x^2+1)\,\mathrm dx$
$=\left(\dfrac13x^3+x\right)\bigg|_0^3$
=12

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Ответ:

alfarodougoy8lvt

08.02.2022

Mathematics

z=7/2

Step-by-step explanation:

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Find the arc length of the curve: y = 1/3(x^2+2)^(3/2). from x=0 to x=3

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