Question

∫¹∫²x² dx

Answer 1

Using the formula

$$\int x^n dx = \frac{x^{n+1} }{n+1}+C$$

$$\int_1^2 x^2 dx = [\frac {x ^{2+1}}{2+1}]_1^ 2$$

$$= [\frac {x^3}{3}]_1^2 = \frac{2^3}{3} - \frac {1^3}{3} = \frac {8}{3} - \frac{1}{3}$$

$$= \frac {7}{3}$$

Answer: $\int_1^2 x^2 dx = \frac {7}{3}$