Suppose the interval [4,6] is partitioned into n=4 subintervals. what is the subinterval length δx? list the grid points x0, x1, x2, x3, x4. which points are used for theleft, right, and midpoint riemann sums?

If a generic interval is partitioned into subintervals, each one has a length:

In this case, , and , so:

The grid points are given by:

Since and , we have:

The subintervals are of the form :

For the left Riemann sums we will use the left-handed points, namely:

For the right Riemann sums we will use the right-handed points, namely:

For the midpoint Riemann sums we will use the average between the two extrema of each subinterval, given by

This gives the midpoints:

The points used for the midpoint Riemann sums are therefore:

first one because it can't have a fraction in it

step-by-step explanation:

1. perpendicular

2. parallel

3. perpendicular