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
