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

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

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

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

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

Left Hand Riemann Sums

Right Hand Riemann Sums

Midpoint Riemann Sums

Trapezoidal Rule

Summary

Homework Homework Worksheet