• Integral and Differentiation — The fundamental theorem Part 1

  • 2023/07/09
  • 再生時間： 13 分
  • ポッドキャスト

Integral and Differentiation — The fundamental theorem Part 1

無料で聴く

ポッドキャストの詳細を見る

  • サマリー

  • In this episode we are studying a first connection of differentiation and integration. More precisely, we will show that if a Riemann integrable function has an anti-derivative then the computation of the integral comes down to the evaluation of the anti-derivative. The proof provided uses a re-interpretation of the mean value theorem. A reorganisation of the terms involved in the statement of the mean value theorem leads to a relation of function evaluation and the integral of a step function with some height given by the derivative at some point of the function. A telescoping sum and a limit argument concludes the proof. 
    続きを読む 一部表示

あらすじ・解説

In this episode we are studying a first connection of differentiation and integration. More precisely, we will show that if a Riemann integrable function has an anti-derivative then the computation of the integral comes down to the evaluation of the anti-derivative. The proof provided uses a re-interpretation of the mean value theorem. A reorganisation of the terms involved in the statement of the mean value theorem leads to a relation of function evaluation and the integral of a step function with some height given by the derivative at some point of the function. A telescoping sum and a limit argument concludes the proof. 
続きを読む 一部表示

Integral and Differentiation — The fundamental theorem Part 1に寄せられたリスナーの声

カスタマーレビュー：以下のタブを選択することで、他のサイトのレビューをご覧になれます。

Audible.co.jp

Amazon.co.jp
レビューはまだありません。