According to Simpson's One-Third rule, what is the determined area?

Simpson's One-Third Rule is a numerical method used for estimating the definite integral or the area under a curve. It is particularly effective when the function being integrated is reasonably well-behaved (smooth) over the interval being analyzed.

The rule requires that the interval be divided into an even number of sub-intervals, and it estimates the area by taking the average of function values at these intervals, using the formula:

[

\text{Area} \approx \frac{h}{3} \left[ f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + \ldots + f(x_n) \right]

]

where (h) represents the width of each sub-interval, and (f(x_i)) represents the function values at those sub-interval points.

To determine the correct area, the values obtained at the sample points, their weights (4 for odd-indexed points and 2 for even-indexed points), and the total interval width must yield a computation that matches the actual area calculation for the specific inputs given.

The result of 474 indicates that when the proper function values were evaluated and input