Final answer:
The length of the arc of the function f(x) = 2x³/₂ from x = 2 to x = 5 is 27 units.
Step-by-step explanation:
To find the length of the arc of the function f(x) = 2x³/₂ from x = 2 to x = 5, we need to integrate the function over the given interval.
∫[2,5] 2x³/₂ dx
Using the power rule of integration, we can rewrite the function as:
= ∫[2,5] 2x² dx
= [x³/₂] from 2 to 5
= (5³/₂) - (2³/₂)
= 31 - 4
= 27 units.