Final answer:
The length of the parametric curve can be found using the arc length formula for parametric curves.
Step-by-step explanation:
The length of the parametric curve x=1 18t², y=6 12t³ with 0≤t≤3 can be found using the arc length formula for parametric curves:
Length = ∫[a,b] √[dx/dt]² + [dy/dt]² dt
In this case, the length is:
Length = ∫[0,3] √[36t²] + [72t²] dt
Simplifying and evaluating the integral gives:
Length = ∫[0,3] √[108t²] dt
Length = 12 √3.