Question

${\int }_0^2\left[x^2\right]dx=?$.

Answer 1

Consider the given function:

$f\left(x\right)={\int }_0^2\left[x^2\right]dx$

$={\int }_0^2{x}^{2}dx$

$=[\frac{x^3}{3}{]}_0^2$

$=\frac{2^3}{3}-\frac{0^3}{3}$

$=\frac{8}{3}$

Hence this is the answer.