x = 3 + 9t^{2}, y = 6 + 6t^{3}, 0 ≤ t ≤ 4

dx/dt = 18t

dy/dt = 18t^{2}

(dx/dt)^{2}+(dy/dt)^{2} = 18^{2} t^{2} (1+t)^{2}

Sqrt (18^{2} t^{2} (1+t)^{2} = 18t √(1+t)= 18 (1+t)^{3/2} -18(1+t)^{1/2}

Integrating between t= 0 to 4

18 (1+t)^{5/2} /(5/2) -18(1+t)^{3/2} /(3/2) = 18*2/5 *5^{5/2}-18*2/5 -18*2/3 * 5^{3/2} +18*2/3

= 36/3 -36/5+ 36/5 * 5^{5/2}-36/3 * 5^{3/2} = 72/15+36 * 5^{3/2}-12* 5^{3/2} = 24/5+24 * 5^{3/2}

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