arc length of y= -0.1480x^3+1.353x^2-4.068x+5.651 from x=0.2 to x=5.25

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04-02-2017
Mathematics

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arc length of y= -0.1480x^3+1.353x^2-4.068x+5.651 from x=0.2 to x=5.25

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LammettHash LammettHash · Answer 1 · 2017-02-09T17:22:20+01:00

LammettHash LammettHash

09-02-2017

[tex]y=-0.1480x^3+1.353x^2-4.068x+5.651[/tex]
[tex]\implies y'=-0.444x^2+2.706x-4.068[/tex]

The arc length is given by the integral

[tex]\displaystyle\int_{0.2}^{5.25}\sqrt{1+(y')^2}\,\mathrm dx[/tex]

which has a value of about [tex]7.6683[/tex].

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