Let Ln denote the left-endpoint sum using n subintervals and...

Let $L_{n}$ denote the left-endpoint sum using $n$ subintervals and let $R_{n}$ denote the corresponding right-endpoint sum. In the following exercises, compute the indicated left and right sums for the given functions on the indicated interval. $$ R_{6} \text { for } f(x)=\frac{1}{x(x-1)} \text { on }[2,5] $$

Let $L_{n}$ denote the left-endpoint sum using $n$ subintervals and let $R_{n}$ denote the corresponding right-endpoint sum. In the following exercises, compute the indicated left and right sums for the given functions on the indicated interval.
$$
R_{6} \text { for } f(x)=\frac{1}{x(x-1)} \text { on }[2,5]
$$

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Key Concepts

Riemann Sum

A Riemann sum is a method for approximating the area under a curve (or the definite integral) by dividing the interval into smaller subintervals, evaluating the function at specific points within each subinterval, and summing the products of these function values and the widths of the subintervals. This technique helps build an understanding of integration as a limit of summations.

Left-Endpoint Rule

The left-endpoint rule is a specific approach to constructing a Riemann sum by using the left endpoint of each subinterval to evaluate the function. This means that for each subinterval, the value of the function at the left boundary point is multiplied by the width of the interval, and these products are added together to approximate the total area under the curve.

Partitioning an Interval

Partitioning an interval involves dividing the given interval into smaller, equally spaced subintervals. This is crucial for Riemann sums because it establishes the framework for how the function values are sampled and summed, with the interval width often denoted by ?x, calculated as the total length of the interval divided by the number of subintervals.

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