• The Riemann Integral Part 1 - Step functions

  • 2023/06/11
  • 再生時間： 20 分
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The Riemann Integral Part 1 - Step functions

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  • The present episode asks a new question: How can one compute the area under the function graph of a  real-valued function defined on an interval? It turns out that this question is not entirely trivial to answer. In order to have a first clear understanding of some pitfalls, we treat an elementary example case first: We discuss the notion of a step function. Then, the area under function graph — the Riemann integral — can be computed as a sum of certain rectangles. Before we embark to more challenging situations, we shall see that the so defined integral will be well-defined for step functions.
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あらすじ・解説

The present episode asks a new question: How can one compute the area under the function graph of a  real-valued function defined on an interval? It turns out that this question is not entirely trivial to answer. In order to have a first clear understanding of some pitfalls, we treat an elementary example case first: We discuss the notion of a step function. Then, the area under function graph — the Riemann integral — can be computed as a sum of certain rectangles. Before we embark to more challenging situations, we shall see that the so defined integral will be well-defined for step functions.
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