Find the area under the graph of $f$ over the interval $[2,8]$.
\[
f(x)=\left\{\begin{array}{ll}
8 x+9, & \text { for } x \leq 4 \\
61-\frac{5}{2} x, & \text { for } x> 4
\end{array}\right.
\]

Step 1 ：The function is a piecewise function, so we need to split the integral into two parts: one for the interval [2, 4] and one for the interval [4, 8].

Step 2 ：For the interval [2, 4], the function is \(f(x) = 8x + 9\).

Step 3 ：For the interval [4, 8], the function is \(f(x) = 61 - \frac{5}{2}x\).

Step 4 ：We can calculate the area under the graph by integrating these functions over their respective intervals and adding the results together.

Step 5 ：The area under the graph of the function \(f(x) = 8x + 9\) over the interval [2, 4] is \(66\).

Step 6 ：The area under the graph of the function \(f(x) = 61 - \frac{5}{2}x\) over the interval [4, 8] is \(184\).

Step 7 ：The total area under the graph of the function over the interval [2,8] is \(66 + 184 = 250\).

Step 8 ：Final Answer: The area under the graph of the function over the interval [2,8] is \(\boxed{250}\).