# Integral and antiderivative

- Area under the graph as a paradigm
- Definitions (upper and lower sums, integrability).
- Integrability of continuous functions.
- Newton-Leibniz formula: integral and antiderivative.
- Elementary rules of antiderivation (linearity, anti-Leibniz rule of “integration by parts”).
- Anti-chain rule, change of variables in the integral and its geometric meaning.
- Riemann–Stieltjes integral and change of variables in it.
- Integrability of discontinuous functions.

Not covered in the class: Lebesgue theorem and motivations for transition from Riemann to the Lebesgue integral.

The sketchy notes are available here.

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Comment by Deepak Suwalka — Thursday, March 23, 2017 @ 1:48 |