Month: February 2023 (Page 1 of 5)

We will have our first midterm exam this Thursday (March 2).  To prepare for the exam, review the following topics, exercises and examples:

• basic antiderivatives (indefinite integrals) and properties (for sums and constant factors):
  • see https://openstax.org/books/calculus-volume-1/pages/4-10-antiderivatives, esp Example 4.52
  • review WebWork “Integration – Antiderivatives” #1-14 as needed (#1-9 involve power functions; see #10-14 for indefinite integrals involving trig functions and e^x)
  • review quiz solutions (Quiz 2: #1(a)(b))
• definite integrals as area:
  • review WebWork “Integration – Definite Integrals”: #1-2
  • review quiz solutions (Quiz 1: #2)
• computing definite integrals using the Fundamental Theorem of Calculus (i.e., using antiderivatives):
  • see https://openstax.org/books/calculus-volume-2/pages/1-3-the-fundamental-theorem-of-calculus, Examples 1.20 & 1.21
  • review WebWork “Integration – Fundamental Theorem constant bounds”: #1-3, 5
  • review quiz solutions (Quiz 1: #3 and Quiz 2: #2)
• integration by substitution:
  • See https://openstax.org/books/calculus-volume-2/pages/1-5-substitution, Examples 1.30, 1.31, 1.32, 1.34, 1.35
  • review WebWork “Integration – Substitution”: #1-9, 11-16
  • review quiz solutions (Quiz 2: #1(c))
• integration by parts:
  • See https://openstax.org/books/calculus-volume-2/pages/3-1-integration-by-parts, Examples 3.1, 3.2
  • review WebWork “Integration – Integration by Parts”: #1-7, 12-14