1. 4.2
Area
Definition of Sigma Notation
= 14

2. Summation Properties 1.
k is a constant 2.

3. Summation Formulas 1. 2. 3. 4.

4. Evaluate the sum
for n = 10, 100, 1,000, and 10,000
First, factor out the 1/n2 n

5. For n = 10
.65
100
.515
1,000
.5015
10,000
.50015

6. Find the

8. Using Upper and Lower Sums to Find Area (Rectangles)
Find the approximate area of the region bounded by y = x2,
y = 0, x = 0, and x = 2. Let n = 4 be the number of rectangles.
Lower Sum 4
= 1.75

9. Upper Sum 4
= 3.75
The area must be between

10. Now, let n = an infinite number of rectangles
f(x) = x2
base x height