2ydy = 3x²dx
dy = (3x²/2y)dx
dy² = (9/4)(x^4/y^2)dx²
y^2 = x^3
dy² = (9/4)(x^4/x^3)dx²
dy² = (9/4)xdx²

ds = v[(9/4)x + 1]dx

ds = (1/2)v(9x+4) dx

ds = (dx/2)v(9x+4)

So, integrate ds over the interval of x where the arc is defined, and you'll have the arc length.

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