Final answer:
The arc length of the graph of f(x) over the interval [2, 4] is approximately 23.114 units.
Step-by-step explanation:
To calculate the arc length of a function, we can use the formula for arc length given by L = ∫ab √(1 + (dy/dx)2) dx. In this case, the function is f(x) = x3 + 12x, and we need to find the arc length over the interval [2, 4].
First, we find the derivative of f(x) with respect to x, which is f'(x) = 3x2 + 12. Next, we substitute this derivative into the arc length formula and integrate it over the interval [2, 4].
After evaluating the integral, we find that the arc length of the graph of f(x) over the interval [2, 4] is approximately 23.114 units.