Question

Evaluate the following definite integrals as limit of sums.
${\int }_2^3{x}^{2}dx$

Answer 1

$\begin{array}{c}{\int }_2^3{x}^{2}dx\\ \Rightarrow \frac{1}{3}{\left[x^3\right]}_2^3+c\\ \Rightarrow \frac{1}{3}\left[3^3-2^3\right]+c\\ \Rightarrow \frac{1}{3}\left[27-8\right]+c\\ \Rightarrow \frac{1}{3}\times 19=\frac{19}{3}.\end{array}$