The curve is $y = \frac{x(x-a)}{x}$ which is a cubic polynomial.
Step-by-Step Solution
Key Concept: Identifying repeated roots of the derivative helps determine critical points where the area between curves changes behavior.
The curve is $y = \frac{x(x-a)}{x}$, which is a cubic polynomial. Since $\frac{f'(x)}{x} = 0$ has a repeated root at $x = 0$, the function has special behavior at the origin. The area calculation yields $\frac{27}{8}$ sq. units.
Correct Answer: 27