Find the length of the curve y=3x^3/2 from x=0 to x=5/9

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01-02-2017
Mathematics

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Find the length of the curve y=3x^3/2 from x=0 to x=5/9

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LammettHash LammettHash · Answer 1 · 2017-02-07T20:16:17+01:00

LammettHash LammettHash

07-02-2017

[tex]y=3x^{3/2}\implies y'=\dfrac92x^{1/2}[/tex]

The length of the curve is

[tex]L=\displaystyle\int_0^{5/9}\sqrt{1+\left(\dfrac92x^{1/2}\right)^2}\,\mathrm dx=\int_0^{5/9}\sqrt{1+\dfrac{81}4x}\,\mathrm dx=\dfrac{335}{243}[/tex]

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