Evaluate the following integral: $\int_{2}^{3} x^{2} dx$
(N/A) Let $I = \int_{2}^{3} x^{2} dx$.
We know that the antiderivative of $x^{2}$ is $\int x^{2} dx = \frac{x^{3}}{3} = F(x)$.
By the Second Fundamental Theorem of Calculus,we have:
$I = F(3) - F(2)$
$I = \frac{3^{3}}{3} - \frac{2^{3}}{3}$
$I = \frac{27}{3} - \frac{8}{3}$
$I = \frac{19}{3}$
We know that the antiderivative of $x^{2}$ is $\int x^{2} dx = \frac{x^{3}}{3} = F(x)$.
By the Second Fundamental Theorem of Calculus,we have:
$I = F(3) - F(2)$
$I = \frac{3^{3}}{3} - \frac{2^{3}}{3}$
$I = \frac{27}{3} - \frac{8}{3}$
$I = \frac{19}{3}$
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