Final answer:
To find the length of the curve, use the arc length formula for parametric curves and integrate.
Step-by-step explanation:
To find the length of the curve y = 4x^(3/2), we can use the arc length formula for parametric curves. The formula is given by:
L = ∫ sqrt( (dx/dt)^2 + (dy/dt)^2 ) dt
In this case, we can consider x as the parameter and differentiate y with respect to x to find dy/dx. Then, substitute these values into the arc length formula and integrate.