Respuesta :

LammettHash
[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]