5.2. Properties of the Riemann integral

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Lecture course: Mathematics for Physicists 1 (IPSP), Winter term 2020/21, University of Leipzig.

Lecturer: Dr. Stephan Mescher

Contents of this video: integrals and algebraic operations, composition of continuous and Riemann-integrable functions are R.-integrable, mean value theorem for integrals.
  1. Stephan Mescher
  2. Lecture
  3. Mathematics
  4. University of Leipzig
  5. Uni Leipzig
  6. Universität Leipzig
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26:21 I don´t quite understand, how that inequality is derived:
The left-hand-side is subtracting the "smallest" value of a function (the composition in this case) in an interval from its "biggest" one. That should result in a "maximum" value.
The right-hand-side lets x and y vary freely within that interval and is looking for the "maximum" value of the differences of that same function for all possible x and y. Wouldn´t it find the same difference as on the left side? Why would it ever be bigger?

cartmansuperstar