Step 1 :Define the function \(f(x) = \frac{2}{x} + 2\).
Step 2 :Define the interval from \(x = 1\) to \(x = 9\) and the number of subintervals \(n = 4\).
Step 3 :Calculate the width of each subinterval \(h = \frac{b - a}{n} = 2.0\).
Step 4 :Calculate the midpoints of each subinterval, which are \([2.0, 4.0, 6.0, 8.0]\).
Step 5 :Evaluate the function at the midpoints and multiply by the width to get the area of each rectangle. The areas are \([6.0, 5.0, 4.67, 4.5]\).
Step 6 :Sum up all the areas to get the total area. The total area is approximately 20.17 when rounded to two decimal places.
Step 7 :Final Answer: The area under the graph of \(f(x)\) and above the \(x\)-axis, approximated using the midpoints, is \(\boxed{20.17}\).