Question

$\int_{1}^{2} x^{2} dx =$

Answer 1

$\frac{7}{3}$

Answer 2

We compute the integral:

$$\int_{1}^{2} x^2 \,dx = \left[\frac{x^3}{3}\right]_{1}^{2} = \frac{2^3}{3} - \frac{1^3}{3} = \frac{8}{3} - \frac{1}{3} = \frac{7}{3}.$$

Antiderivative of $x^2$ is $\frac{x^3}{3}$. Evaluate at bounds 2 and 1, then subtract.