Class Info

  • Date: Mon, Sept 11
  • Meeting Info: 10a-11:40a, N719

Topics

  • Reviewed techniques for finding antiderivatives (“indefinite integrals”) and notation for area under a curve (“definite integrals”)
    • we will focus on the connection between these two concepts: calculating areas via antiderivatives – the Fundamental Theorem of Calculus (FTC)
  • Examples from “Integration – Definite Integrals” WebWork set
  • Area under the curve y = 3x over the interval [2, 8] in three different ways: (1) area of a triangle + area of a rectangle, (2) area of large triangle – area of small triangle, and (3) using the FTC:
  • Discussed how the definite integral computes “net signed area” – area under the x-axis “counts negatively”
  • See OpenStax Sec 1.2, Figure 1.18, Example 1.9, Checkpoint 1.9:

To-Do After Class

  • Start working through “Integration – Definite Integrals” (due Monday eve, Sept 11)
    • You can use the FTC, i.e., use antiderivatives, whenever possible
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