• The Riemann Integral Part 2 - Riemann integrability

  • 2023/06/18
  • 再生時間： 22 分
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The Riemann Integral Part 2 - Riemann integrability

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  • In this episode, we introduce the class of Riemann integrable functions. At the heart of the definition lies the wish to extend the intuitive notion for the integral of step functions on closed and bounded intervals to functions for which one can approximate the area between the function's graph and the x-axis by areas of rectangles. We then discuss that all continuous functions on a closed and bounded interval are Riemann in fact integrable - a fact that heavily relies on the property of uniform continuity.
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In this episode, we introduce the class of Riemann integrable functions. At the heart of the definition lies the wish to extend the intuitive notion for the integral of step functions on closed and bounded intervals to functions for which one can approximate the area between the function's graph and the x-axis by areas of rectangles. We then discuss that all continuous functions on a closed and bounded interval are Riemann in fact integrable - a fact that heavily relies on the property of uniform continuity.
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