Area+Under+or+Between+Curves

Riemann Sums
 Riemann sums can be used on the left, right, or middle. If it is a left Riemann sum the corner of the rectangle goes on the first point on the function or on the more left side. If it is a right Riemann sum it goes on the second point in the group. If it is a middle Riemann sum, it goes in the middle of the two points. After you find all the areas of each rectangle, add them up. That is an ESTIMATION of the area under the curve.

 This is similar to Riemann sums only instead of rectangles, one uses trapazoids. This gives a more accurate ESTIMATION of the area under the curve.

﻿ ﻿Integrals
Integrals are the area under the curve. See integral rules pages for clarification on how to do integrals. Definite integrals give one a specific number that is the area under the curve. Indefinite integrals will only give you an equation of the area under the curve.   Area Between Curves You take the top function and subtract it from the bottom function and then take the definite integral of that equation, with a and b being the domain over which you are evaluating the area between the curves. The tricky part is finding out which equation is the top one. The easiest way to do this is to graph them on a graphing calculator. If the functions cross during the domain you are looking at, you are going to need to evaluate each part seperately so that the bottom function is always subtracted from the top function.

"Riemann Sum." //Wikipedia, the Free Encyclopedia//. Web. 26 May 2011. .