1. Section 4.3 Day 1 Riemann Sums and Definite Integrals AP Calculus BC

2. Learning Targets  Define Riemann Sums  Conceptually connect approximation and limits  Evaluate left hand, right hand and midpoint Riemann Sums of equal and unequal lengths from graphs & tables  Evaluate approximations using the trapezoidal rule  Define a definite integral  Evaluate a definite integral geometrically and with a calculator  Define an integral in terms of area  Apply properties of a definite integral

3. Set up Foldable  Cover: Riemann Sums & Definite Integrals  Left Hand Riemann Sum  Right Hand Riemann Sum  Midpoint Riemann Sum  Trapezoidal Rule  Conceptual Riemann Sum

4. Warm-Up Write the first mathematical symbol that comes to your mind when you hear the following words… 1.) Function Value 2.) change in x 3.) area 4.) sum 5.) closer & closer to… 6.) # of subintervals 7.) incomprehensibly large

5. Conceptual Riemann Sums  Think of a situation where the approximation of the area under a curve with rectangles can be the exact area under the curve.  As the number of rectangles approximating the area under the curve gets closer to infinity, the area under the curve becomes closer to the exact area. The number of rectangles as a limit to infinity will produce the exact area under the curve

6. Left Hand Riemann Sums

8. 02379 36768

9. Right Hand Riemann Sums

11. 02379 36768

12. Midpoint Riemann Sums

14. 0510152025303540 7.09.29.57.04.52.4 4.37.3

15. Trapezoidal Rule

17. 025910 6660524443

18. Summary

19. Homework Homework Worksheet