1. 4.2 Area

2. Sigma Notation where i is the index of summation, a i is the ith term, and the lower and upper bounds of summation are 1 and n respectively The sum of n terms a 1, a 2, a 3, ….an is written

3. Examples:

4. Properties of Summations Summation Formulas

5. Example 1: Find the sum of the first 100 integers.

6. Example 2: Summation Practice

7. Example 3: Limits Review

8. Example 4: Limit of a Sequence

9. Warm-up

10. Definition of the Area of a Rectangle: A=bh Take a rectangle whose area is twice the triangle: A=1/2 bh For any polygon, just divide the polygon into triangles.

11. Area of Inscribed Polygon < Area Circle < Area of Circumscribed Polygon

12. Area of a Plane Region Find the area under the curve of Between x = 0 and x = 2

13. Area of a Plane Region—Upper and Lower Sums Begin by subdividing the interval [a,b] into n subintervals, each of length Endpoints of the subintervals: Because f is continuous, the Extreme Value Theorem guarantees the existence of a min and a max on the interval.

14. Sum of these areas= lower sum Sum of these areas= upper sum

15. Example: Find the upper and lower sums for the region bounded by the graph of

17. Example: Find the area of the region bounded by the graph of