Calculus: Area. Riemann sums. Definition of the definite integral as a limit of Riemann sums. Expressing a definite integral as a limit of Riemann sums. Evaluating a definite integral by interpreting it in terms of areas.
This video series covers how to express a definite integral as a limit of Riemann sums. The series does not cover how to evaluate a definite integral as a limit of Riemann sums.
This is a recording of a tutoring session, posted with the student's permission.
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For a document containing some of the problems discussed in video (2), click here:
http://www.freelance-teacher.com/Area__Riemann_sums__Definite_integrals_problems2.pdf
TABLE OF CONTENTS
VIDEO (1)
Review of derivatives as a limit of approximations
Approximating areas with rectangles over subintervals
VIDEO (2)
0:00 Problems
41:40 Riemann sums
1:18:30 Σ notation
1:24:30 Definition of the definite integral as a limit of Riemann sums
VIDEO (3)
Expressing a definite integral as a limit of Riemann sums
Evaluating a definite integral by interpreting it in terms of areas
VIDEO (4)
Homework
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