In Sections 13.2 and 13.3, you will be calculating areas using an approximate methods called Riemann Sums. For small numbers of data points or small numbers of rectangles, we can easily calculate a Riemann Sum by hand. However, as the number of rectangles gets larger (like more than 8 rectangles) the task becomes overwhelming. Luckily, there are online calculators that make the task trivial.
Click here to go to the WolframAlpha website.
To be able to use this calculator, you need to know the formula for the function f (x), where the sums will run, the number of rectangles, and whether the rectangle will touch the function on the left or right hand side.
In the image above, the function we are finding the Riemann sum for is f (x) = 2x+1 and we are forming rectangles from x = 1 to x = 4. In this case we have chosen to use 3 rectangles that touch on the right side of the rectangles. This type of Riemann Sum would be referred to as a Right Hand Sum (RHS).
If we were to have the rectangles touch on the left hand side, we would have a Left Hand Sum (LHS). In this case we would change the “taking the samples at the Right” to “taking the samples at the Left”
Make sure you choose Replot after you make any changes.
We can double the number of rectangles to 6 to get
If you continue to increase the number of rectangles with LHS or RHS, the estimate of the area will get closer and closer to the actual area (which we can find using geometry).
Use this tool in your homework to help relieve the drudgery of adding up all of the sums. Keep in mind that if you are given data points or a graph, you will have to work out the sums by hand.