Final answer:
The length of the curve y²=4(x-4)³ can be found using calculus and the arc length integral formula, however specific bounds are necessary to solve for a numerical result.
Step-by-step explanation:
To find the length of the curve y²=4(x-4)³, one would typically need to use calculus, specifically arc length integrals. However, your question doesn't provide specific bounds for x or y, which are necessary to compute the definite integral for arc length. If you can provide these bounds, the integral for arc length in Cartesian coordinates is given by:
L = ∫ √(1+(dy/dx)²) dx
First, we would differentiate y with respect to x, square the result, add one, take the square root of this sum, and then integrate over the specified interval.
A complete solution requires more detailed information, including the specific interval over which you want to find the length of the curve. Without these details, we can't provide a numerical answer. Remember, specifying the domain of x or the range of y is crucial for finding a concrete solution to this problem.