Final answer:
To find the arc length of the curve y = x^³/² from x = 0 to x=4, you can use the formula As = ∫(sqrt(1 + (dy/dx)²)) dx and apply it to the given curve.
Step-by-step explanation:
The arc length of a curve can be found using the formula:
As = ∫(sqrt(1 + (dy/dx)²)) dx
Applying this formula to the given curve y = x^(3/2) from x = 0 to x = 4, we have:
As = ∫(sqrt(1 + (3/2)x^(1/2)²)) dx
Integrating this expression will give us the arc length of the curve.