Riemann sums and sigma notation

The  exercise appears under the Integral calculus Math Mission. This exercise formally explores the Riemann sum and practices sigma notation.

Types of Problems
There are three types of problems in this exercise:


 * 1) Select the statements that are true: This problem has a graph and several rectangles drawn in that approximate the area. The student is asked to select true statements about the picture from a multiple select list.Rsasn1.png
 * 2) Select the correct sum: This problem presents a function and it's approximation with several rectangles. The student is asked to select the sum that correctly models the rectangles in the picture.Rsasn2.png
 * 3) Determine which sum is which in the picture: This problem presents several Riemann sum approximations to function. The student is asked to select which sum corresponds to which picture.Rsasn3.png

Strategies
Knowledge of sigma notation and different Riemann approximations are encouraged to ensure success on this exercise.
 * 1) The LRAM uses the left endpoint, the RRAM uses the right endpoint and the MRAM uses the midpoint of intervals.
 * 2) Figuring out the first (or last) element of the sum can rule out incorrect Riemann sums efficiently.
 * 3) Different point selection can create better estimates to area, and the shape of the function can help determine which are best.

Real-life Applications

 * 1) Geometrically an integral can be used to find area and volume formulas.
 * 2) Approximate area is useful in numerical analysis and other situations where antiderivatives are difficult or impossible.