## Riemann sums to definite integral conversion

In the most recent tutorial there is a question about converting a Riemann sum to a definite integral, and it seems to be tripping up quite a few students. I wanted to run through one of the calculations in detail so you can see how to answer such a question.

Let’s look at the example:

There are many ways to tackle such a question but let’s take one particular path. Let’s start by the fact that when the limit is defined, the limit of a sum is the sum of the limits. We can split up our expression into 3, which looks like:

Let’s tackle each of these separately. Let’s look at the first term:

Well, we can take the factor of 13 outside the front of the whole thing to start with, along with the factor of 9, and this will give

We see here that we have a sum of terms, and a factor which looks like in each term.…