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Riemann Sums by Mind Map: Riemann Sums

1. Lower Sum

2. Caluclation of the real Area

2.1. We will use the Upper Sums ON Blackboard

2.1.1. We will Calcuate the general formula for any n

2.1.2. We calculate the limit when n is going to infinity to get the area

2.2. Play more:

3. The Problem

3.1. The Graph Step 1: Make a large, careful graph of y = x² - x + 1 on the interval (1,9).

3.2. The Area

3.3. We want to use 8 rectangles Step 2: Divide the interval (1,9) into n = 8 equal subdivisions, each subinterval having width Δx=(9−1)/8=1, Make a table showing the intervals, their left endpoints xL midpoints xM, and right endpoints xR, and the values of f(x) at each of these points

3.3.1. Upper Sum

3.3.2. Step 3: For each subinterval, draw rectangles with base on the x-axis and height f(xL),f(xM), and f(xR) respectively.

3.3.3. Upper vs Lower

3.4. Play with the number of rectangles

3.5. The Table we want

3.6. Next steps

3.7. Final Table

4. More Problems