What is the area determined using the trapezoidal rule?

The trapezoidal rule is a numerical method used to estimate the area under a curve when dealing with a set of data points. This method works by approximating the region under the curve as a series of trapezoids rather than rectangles, which can provide a more accurate approximation.

To determine the area using the trapezoidal rule, one typically uses the formula:

[

\text{Area} = \frac{(b - a)}{2} \times (f(a) + f(b))

]

where ( a ) and ( b ) are the endpoints of the interval, and ( f(a) ) and ( f(b) ) are the function values at those endpoints. The area can be refined further by dividing the interval into smaller sections and summing up the areas of the trapezoids formed.

The accuracy of the trapezoidal rule often exceeds that of other basic numerical methods, especially for smooth and continuous functions. In your case, if the computation done using this method results in an area of 590, it is concluded that this is likely calculated correctly based on the trapezoidal rule's approach.

Thus, when the trapezoidal rule is applied correctly, it can yield the value of