Use a limit of Riemann sums to evaluate the definite integral.
$\begin{aligned} \int_{3}^{5} (4 x - 1) d x & = lim_{n \to \infty} \sum_{i = 1}^{n} \\ = lim_{n \to \infty} \\ = \end{aligned}$

Hint: This list of summation rules may be helpful.

Answer

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Answer

The final answer is $30$

Steps

Step 1 ：Set up the Riemann sum for the function $f (x) = 4 x - 1$ over the interval $[3, 5]$

Step 2 ：Use the limit definition of the definite integral, taking the limit as $n$ approaches infinity of the sum of $f (x_{i}) \times Δ x$

Step 3 ：Use the right endpoint of each subinterval as the sample point

Step 4 ：Calculate the definite integral using the limit of Riemann sums

Step 5 ：The final answer is $30$