Riemann Sums on a graphing calculator

To calculate Riemann sums on a calculator using 3 rectangles and the midpoint method, we need to have several inputs, and calculations. First, the curve as a function of x must be put into the calculator, and saved as a string. Afterwards, we can learn the interval over which we are finding the area, saving the lower bound as A and the upper bound as B. This portion of the code looks like this:



After finding all the information, we simply plug these numbers into the formula to find the Riemann sum using 3 intervals and using the midpoints of these intervals to find the height of the rectangles we will sum to find the area under the curve. To find this, we use the information from the previous inputs to find the 3 midpoints that of our intervals. These will be found by using the lower bound added to the length of the interval multiplied by 1/6, 3/6, and 5/6 to find the 3 midpoints respectively.



After we have the midpoints, we simply put these values into F(x) to find the height of our rectangles, and multiply these by the width of the rectangle, and sum the areas found this way.



This well give us an estimate of the area under a curve. This is not a very good estimate, because it only has 3 rectangles. As the number of rectangles increases, the area under the curve becomes more and more precise. Still, finding this area can give us a very good idea of the area under the curve, if not a very precise answer. The midpoint is generally a good way to do it, but depending on the shape of the curve, a left endpoint or a right endpoint estimate may be more accurate. It is uncommon for the midpoint to be the least accurate method.



Discussion of Benefits and Hindrances of technology for Riemann Sums Problem and Crossing Ladder Problem-

During the Riemann sums problem, technology may seem like a hindrance right away, because it takes much longer to write the code for the problem than to just do the calculations yourself. But in the long term, writing the code and using the technology is a huge benefit to save time and ensure accuracy on multiple calculations.

For the crossing ladders problem, technology was definitely a benefit, and not really a hindrance at all. After finding a complicated series of formulas, you could just put them into wolfram alpha, and know that the equation was solved correctly. Also, after finding the formula, you could just change the numbers and find the answer to any similar problem, simply by typing in the equation with the correct numbers.