Which part of the trapezoidal rule formula represents the first measurement?

In the trapezoidal rule, the formula is used to estimate the integral of a function. This estimation involves dividing the total area under the curve into trapezoids instead of rectangles. To clarify how the formula structures its calculations, we can break it down.

The part of the formula that corresponds to the first measurement is the term that represents the function's value at the starting point of the interval over which you are integrating. This value reflects the height of the first endpoint of the trapezoid. In the context of the options provided, this term is denoted as (Df), which typically refers to the function's value (or the change in the function's value) at the first endpoint. By incorporating this measurement, the trapezoidal rule effectively establishes the foundation upon which the entire estimate is built, allowing for a more accurate approximation of the area under a curve.

Thus, (Df) is essential as it marks the starting point of the sum used in the trapezoidal calculation, ensuring that the overall area estimation accounts for the function's behavior at the interval's beginning.