Short Calculus pp 134-152 | Cite as


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


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.



Continuous Function Small Interval Fundamental Theorem Small Rectangle Geometric Intuition 
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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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