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Verified Answer :

LammettHash

\(y=3x^{3/2}\implies y'=\dfrac92x^{1/2}\)

The length of the curve is

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

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