Question

Evaluate the following definite integrals as limit of sums.
${\int }_{-1}^1{e}^{2x}dx$

Answer 1

$\begin{array}{c}{\int }_{-1}^1{e}^{x}dx\\ \Rightarrow {\left[e^x\right]}_{-1}^1+c\\ \Rightarrow \left[e^1-e^{-1}\right]+c\\ \left(\frac{e^2-1}{e}\right).\end{array}$