Evaluate the integral: ∫limits_2^3 x^2 dx

The correct answer is Option (3) → $\frac{19}{3}$

Let $I = \int\limits_{2}^{3} x^2 \, dx$. Since $\int x^2 \, dx = \frac{x^3}{3} = F(x)$,

Therefore, by the second fundamental theorem, we get

$I = F(3) - F(2) = \frac{27}{3} - \frac{8}{3} = \frac{19}{3} \text{}$