Example 7.2.5. Best fitting area function for a linear function.
Repeat the last example, finding the area under \(f(x)=6x\text{,}\) with Excel.
Solution.
With a linear function we have use the following to produce an area function.

Column C has our list of \(t\) values in the center of each interval. Column D has the value of \(f(t)\) evaluated at those points. The area of the rectangle is the height \(f(mid_n)\) times the width,
Interval width
. SumArea
is our running area function. When we plot the area function, we have something that seems to be quadratic with leading coefficient \(c/2\) and very small linear and constant coefficients. In fact, the linear and constant coefficients are zero up to a rounding factor for numbers of the size we are using.