Section 7.2 - Antidifferentiation by Substitution

Essential Question(s): 

How is substitution used with definite and indefinite integrals?​

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Follow these three steps to complete this "flip" lesson.

STEP 1: Preparation 
Title your spiral with the heading above and copy the essential question(s).

STEP 2: Vocabulary & Examples 
Answer the follow questions. They address examples, vocabulary, rules, theorems, corollaries, procedures, and/or postulates. Following a Cornell notes format, the questions should be written in the left-hand column and with the answers to the right of the question. Make sure to write enough to answer the question.

Indefinite Integrals

1. What is an indefinite integral? (pg 340)
2. How are definite integrals and an indefinite integrals different? (pg 340)
3. How do you evaluate an indefinite integral? (Ex 1 pg 340)
4. What are the Formulas/Properties for indefinite integrals? (pg 341)
5. Why are absolute values needed? (pg 341 sidebar of Ex 2, and Ex 2)

Leibniz Notation and Antiderivatives

1. ​How does the differential matter? (Ex 3 pg 342)

Substitution in Indefinite Integral

1. What is substitution in indefinite integrals? (pg 342,between Ex 4 & 5 pg 343)
2. How do you use substitution with indefinite integrals? (Ex 4, 5, 6 pg 342 - 344)
3. How do you setup a indefinite integral substitution using a trigonometric identity? (Ex 7 pg 344)

Substitution in Definite Integrals

1. How do you use substitution in a definite integral? (Ex 8 pg 345)
2. How does the absolute value apply when using substitution in a definite integral? (Ex 9 pg 345)

STEP 3: Reading
Read the following page(s) and take any extra notes as needed.

• Read pages 340 - 346.
• Make sure to read the paragraphs between the examples and sidebar snippets.