Evaluate: $\int\limits_{1}^{3} (x - 1)(x - 2)(x - 3) dx$

$0$

The correct answer is Option (3) → 0 ##

Let $I = \int\limits_{1}^{3} (x - 1)(x - 2)(x - 3) dx$

$= \int\limits_{1}^{3} (x^{3} - 6x^{2} + 11x - 6) dx = \left[ \frac{x^{4}}{4} - \frac{6x^{3}}{3} + \frac{11x^{2}}{2} - 6x \right]_{1}^{3}$

$= \left[ \frac{81}{4} - \frac{162}{3} + \frac{99}{2} - 18 - \left( \frac{1}{4} - \frac{6}{3} + \frac{11}{2} - 6 \right) \right] = 0$