e integral using the following values. \[ \begin{array}{l} \int_{2}^{8} x^{3} d x=1,020, \int_{2}^{8} x d x=30, \int_{2}^{8} d x=6 \\ \int_{2}^{8}\left(4 x-\frac{1}{10} x^{3}\right) d x \end{array} \]

Step 1 ：We are given the integral of \(x^3\), \(x\), and \(1\) over the interval \([2, 8]\).

Step 2 ：We can calculate the integral of the function \(4x - \frac{1}{10}x^3\) by subtracting the integral of \(\frac{1}{10}x^3\) from the integral of \(4x\).

Step 3 ：The integral of a sum of functions is equal to the sum of the integrals of the functions.

Step 4 ：Substitute the given values into the equation: integral_x3 = 1020, integral_x = 30, integral_1 = 6.

Step 5 ：Calculate the integral of the function, which is 18.0.

Step 6 ：The integral of the function \(4x - \frac{1}{10}x^3\) over the interval \([2, 8]\) is \(\boxed{18}\).