Answer
$A=\lim\limits_{n \to \infty}\sum_{i=1}^n\frac{5x_i+5\ln x_i}{n}$
Work Step by Step
Using the Definition 2,
$A=\lim\limits_{n \to \infty}\sum_{i=1}^nf(x_i)\Delta x$ where $\Delta x=\frac{\text{upper bound - lower bound}}{n}$
Find $\Delta x$ and simplify:
$\Delta x=\frac{8-3}{n}=\frac{5}{n}$
Then,
$A=\lim\limits_{n \to \infty}\sum_{i=1}^n(x_i+\ln x_i)\cdot \frac{5}{n}$
$A=\lim\limits_{n \to \infty}\sum_{i=1}^n\frac{5x_i+5\ln x_i}{n}$