This calculus video tutorial explains how to use Riemann Sums to approximate the area under the curve using left endpoints, right endpoints, and the midpoint rule. It also shows you how to calculate the area by evaluating the definite integral by using the process associated with sigma notation & Limits at Infinity known as the definition of the definite integral. This video contains plenty of examples and practice problems.

Here is a list of topics:

1. Area Under Curve Problem

2. Using Rectangles to Estimate the Area of the Shaded Region

3. Riemann Sums - Left Endpoints and Right Endpoints

4. Midpoint Rule - Best Estimation

5. Over approximation vs Under Approximation - Left & Right Endpoints - Increasing and Decreasing Functions

6. Area of Rectangle - f(x) / height vs delta x / width

7. Definition of the Definite Integral

8. Finding the Area Using the Definite Integral

9. Width of Subinterval Formula & Number lines

10. Graphing the Rectangles Using Midpoint, Left and Right Endpoints

11. Evaluating the Definite Integral Using Sigma Notation & Limits at Infinity

12. Riemmann Sums & Area Approximation

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