Question

Calculate left and right Riemann sums for f(x)= (x^2)-1 on [2,4] when n=4

Answer 1

You need some numbers before you can write down the Riemann-sums:

First, n=4.
This means the interval [2,4] is chopped up into 4 equal parts, of width 0.5 (=\(\Delta\) x).
The 4 parts are: [2, 2.5], [2.5, 3], [3, 3.5] and [3.5, 4].

Then, you'll need a starting number, x. The left sum takes the left part of each interval.
So: x= 2, 2.5, 3 and 3.5.

Now calculate f(x) for each of these x-values, and multiply each f(x) with 0.5 (=\(f(x) \Delta\)\(x\)).

Add these four numbers, which are the areas of the rectangles under the graph.
Now you have the left Riemann-sum.

To calculate the right sum, you only have to use the right side of each interval for x, so that would be 2.5, 3, 3.5 and 4. The rest is the same.

Good luck!

Answer 2

This is a drawing that could help a little...