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
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