The Integral
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.
- The Definite Integral of a Continuous Function - Practice with The Definite Integral of a Continuous Function.
- The Function Integral of f(t) dt - Practice with The Function Integral of f(t) dt.
- Table of Integrals - Table of a bunch of different integrals.
- Special Functions - Integrals of some special functions.
- What is a definite integral?
- How do you find an integral?
- What is an augmented partition of a closed interval?
- What is a Riemann Sum?
- What is the norm of a partition?
- When is a function integrable on an interval?
- How do you find the integral of a piecewise function?
- What is geometric evaluation of integrals?
- How does symmetry affect integrals?
- What is the Interval Additivity Property?
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Staff Review
This video explains what an integral is using Riemann Sum notation. It then goes on to explain why some integrals are positive and some are negative, and what an integral is actually finding. Some interesting examples are used in this video. The video also shows how you can find the integral of certain functions by looking at the graph and finding the area of the geometric shape. This is a pretty good lesson for learning and understanding what an integral is and how to compute it.
