1. 5/16/2015 Perkins AP Calculus AB Day 5 Section 4.2

2. Area Under a Curve Find the area of the region bounded by y = f(x), the x-axis, x = a, and x = b. We call it the Lower Sum. We call it the Upper Sum. Approximate the area by creating rectangles of equal width whose endpoints are on f(x). Each right endpoint is on f(x) Each left endpoint is on f(x) This over-estimates the area under the curve… This under-estimates the area under the curve… n = # of rectangles Each method is called a Riemann Sum.

3. How do we make these approximations for the area under a curve more accurate? Use more rectangles. (Always choose whichever sum involves right endpoints.) The Limit Definition for finding the area under a curve: or

4. Find the area beneath (above the x-axis) in the interval [1,3]. a. Use 1 rectangle. b. Use 2 rectangles. If a specific number of rectangles is given, it is often easier to find the area without using sigma!

5. Find the area beneath (above the x-axis) in the interval [1,3]. c. Use the limit definition.

7. Perkins AP Calculus AB Day 5 Section 4.2

8. Area Under a Curve Find the area of the region bounded by y = f(x), the x-axis, x = a, and x = b. Approximate the area by creating rectangles of equal width whose endpoints are on f(x).

9. How do we make these approximations for the area under a curve more accurate? The Limit Definition for finding the area under a curve:

10. Find the area beneath (above the x-axis) in the interval [1,3]. a. Use 1 rectangle. b. Use 2 rectangles.

11. Find the area beneath (above the x-axis) in the interval [1,3]. c. Use the limit definition.