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.