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Short Calculus pp 134-152 | Cite as

Integration

  • Serge Lang
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

In this chapter, we solve, more or less simultaneously, the following problems:
  1. (1)
    Given a function f(x), find a function F(x) such that
    $$ F'(x) = f(x). $$
    This is the inverse of differentiation, and is called integration.
     
  2. (2)

    Given a function f(x) which is ≧ 0, give a definition of the area under the curve y = f(x) which does not appeal to geometric intuition.

     

Keywords

Continuous Function Small Interval Fundamental Theorem Small Rectangle Geometric Intuition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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