Focus Area: FTOC Created by Mr. Lajoie

5.3 The Fundamental Theorem of Calculus, Part 1 2  Part One:

Ease & Precision in Evaluating Definite Integrals 3  The usefulness of the Fundamental Theorem of Calculus, particularly Part One, is that we can now evaluate definite integrals with tremendous ease, as compared to our work in the Shuttle Launches Project with trying to find the area using geometric approximation.  More importantly, the Fundamental Theorem of Calculus allows us to determine the exact, precise value of the definite integral—and thus, the net signed area—as compared to the estimates we sufficed ourselves with when using rectangular approximation methods.

An Investigation of Sorts… 4

A Comparison 5  What do you notice? Take-away from this slide: The constant term that we always attach when we evaluate indefinite integrals cancels when we evaluate the definite integral, so we do not need to attach “C” if we are evaluating a definite integral!

Example1 6