A number of you have asked me if there are tools that allow you to calculate left or right hand sums (Riemann sums). If you know the function which you want to approximate the area under, YES! There are many available online…a good one is this calculator from Wolfram Alpha.

If you supply the function, the starting and ending point of the area, and the number of rectangles, this app will find the left, right, and midpoint sums. Simply put in the function, supply the proper options, and select Replot.

Here is an example of left hand sums with 2 rectangles for the function $latex \displaystyle f(x)={{x}^{2}}+1$.

Under the rectangles, you’ll see the estimated area as well as the actual area (which we’ll find in later sections. Here is the same area found with right hand sums.

You can also select midpoint sums.

You can also increase the number of rectangles to give better estimates. Here is a left hand sum with 8 rectangles.

You can easily increase the number of rectangles as needed.