In this lesson on the integral, we learn about the definition of the integral and its application in finding signed area. We explore how Riemann sums can be used to approximate the area under a curve, and how the limit of these sums can give us the exact area. We also discover how to evaluate integrals geometrically, using the area of shapes like rectangles and trapezoids. Through examples and explanations, we see how integrals can be used to find net area, and how they can be applied in real-world scenarios.
Definition of the integral. Signed area. Geometric evaluation and symmetries. Interval additivity property.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.