Evaluate the Riemann sum for (x) = x3 − 6x, for 0 ≤ x ≤ 3 with six subintervals, taking the sample points, xi, to be the right endpoint of each interval and please explain, using a graph of f(x), what the Riemann sum represents.

My cousin needs help with her homework but I have no idea what this stuff is about. If someone could please help us and explain the work so that I can maybe try and remember how to help her, that would be nice :)

1 answer

break the interval into six parts,
zero to .5, .5 to 1, etc.

then calculate the function in those intervals, you can choose the left number, the right number, or the center number. Lets do it on the RIGHT endpoint
first calculate f(.5), then f(1), and so on.
Each of those values are multiplied by the width of the interval, in our case .5.

Now take those six areas (width x height), add them.