Definite Integration and the “Need to Know” Principle

  • Definite Integration and the “Need to Know” Principle

    Robert Gethner
    Ever since I learned, in my first calculus course, how to evaluate definite integrals using trigonometric substitution, I have been puzzled by the standard method of computing the limits of the transformed integral. Recently, I have come to terms with the problem and have begun to clarify a pedagogical dilemma that has presented itself several times in my calculus classroom. An important issue that teachers face with some regularity throughout the curriculum is this dilemma: How do we introduce to students new ideas that they need but are not yet ready to fully comprehend? I have formulated what I call the “need to know” principle, which I use to think about the challenge of presenting difficult ideas.
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