We have:
\(A = \frac{1}{2} \int_{4}^{6} x \cdot (6x - x^2) \, dx.\)
Calculating the integral:
\(A = \frac{1}{2} \int_{4}^{6} (6x - x^2) \, dx = \frac{76}{3}.\)
Multiplying by 12:
\(12A = 12 \times \frac{76}{3} = 304.\)
The Correct answer is: 304
Match List-I with List-II: List-I