MA101: Single-Variable Calculus I

7.2: The Fundamental Theorem of Calculus

• The Fundamental Theorem of Calculus is the apex of our course. It explains the relationship between the derivative and the integral, tying the two major facets of this course together. In the previous section, you learned the definition of the definite integral as a limit of a Riemann Sum. The computations were long and involved. In this subunit, you will learn about the Fundamental Theorem of Calculus, which makes computation of definite integrals significantly easier.
  

• Whitman College: David Guichard's "Calculus, Chapter 7: Integration, Section 7.2: The Fundamental Theorem of Calculus" URL

  Read Section 7.2 (pages 149-155). Pay close attention to the treatment of Riemann sums, which lead to the definite integral. The Fundamental Theorem of Calculus explicitly describes the relationship between integrals and derivatives.
  

• Massachusetts Institute of Technology: David Jerison's "The First Fundamental Theorem" and "The Second Fundamental Theorem" Page

  Watch these videos.
  

• Whitman College: David Guichard's "Calculus, Chapter 7: Integration, Exercises 7.2: Problems 7-22" URL

  Work through problems 7-22 for Exercise 7.2. When you are done, check your answers against Appendix A.