How do you do lram

This is sort of how definite integrals in the next section work; they are like Riemann Sums with an infinite number of rectangles. They each have a base of. We could calculate each area individually and add them, but the length is the same for each one, at. We can add the heights together, and then multiply taht by. Since it is an RRAM Riemann Sum, we will use the right corners of the rectangles to reach the function: Now, we need to find the values for the right sides of each rectangle, since these will be their heights.

Plugging these into our function and solving gives: So, the heights of our rectangles are 1,. This is made worse by a curve that is constantly increasing. When a curve goes up and down more, the error is usually less. Adding these up gets 3. We can have a sloped top!

Each slice is now a trapezoid or possibly a triangle , so it is called the Trapezoidal Rule. Adding these up gets 2. Notice that in practice each value gets used twice except first and last and then the whole sum is divided by Note: the previous 4 methods are also called Riemann Sums after the mathematician Bernhard Riemann. An improvement on the Trapezoidal Rule is Simpson's Rule. It is based on using parabolas at the top instead of straight lines.