Let . Use a trapezoid sum with 3 sub-intervals to estimate the area between f and the x-axis on [0,9]. Is this an overestimate or underestimate?
We divide [0,9] into 3 sub-intervals of width 3.The first trapezoid has
The second trapezoid has
The third trapezoid has
Adding up the areas of the trapezoids, we get
71.625 + 58.125 + 31.135 = 160.875.
This is an underestimate, since the trapezoids don't cover the whole area between f and the x-axis on [0,9].