Class Info

• Date: Wed, Sept 13
• Meeting Info: 10a-11:40a, N719

Topics

• discussed the Fundamental Theorem of Calculus (FTC) (calculating definite integrals, i.e., “net signed areas”, using antiderivatives)

Went through more examples from “Integration – Definite Integrals” WebWork set, including using FTC:

FTC example from textbook:

To-Do After Class

• Finish “Integration – Definite Integrals” (due Monday eve, Sept 11)
  • Use the FTC, i.e., use antiderivatives, whenever possible
• Work on “Integration – Fundamental Theorem constant bounds” (due next Thurs, Sept 18)

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)
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• 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:
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• 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:
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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