## Section 6.4 - Fundamental Theorem of Calculus

**Essential Question(s):**

How can the Fundamental Theorem of Calculus be utilized?

**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**

__Copy__and

__define__the following of vocabulary. This can be any tables, properties, theorems, terms, phrases or postulates listed.

__Review__the following examples and

__copy__what is necessary for you. Use the guiding questions for your Cornell notes.

__Fundamental Theorem, Antiderivative Part__

- What are the two outcomes of the Fundamental Theorem of Calculus? (paragraph above Theorem 4 pg 302)
- What is the antiderivative part of the Fundamental Theorem of Calculus? (Theorem 4, pg 302)
- What does the antiderivative part equation of the Fundamental Theorem of Calculus tell us? (pg 303 and text below green box)
- How do you apply the Fundamental Theorem of Calculus? (Ex 1 pg 303)
- How do you apply the chain rule with the Fundamental Theorem of Calculus? (Ex 2 pg 304)
- How do you use the properties of definite integrals and the chain rule with the Fundamental Theorem of Calculus? (Ex 3 pg 304)
- How do you construct a function with a given derivative and value using the Fundamental Theorem of Calculus? (Ex 4 pg 305)

__Graphing the Function__

- Read through this section and take notes as needed. (pg 305 - 307)

__Fundamental Theorem, Evaluation Part__

- What is the evaluation part of the Fundamental Theorem of Calculus? (pg 307)
- What does the evaluation part equation of the Fundamental Theorem of Calculus tell us? (pg 308 and text below green box)
- What is the notation used to evaluate integrals? (sidebar pg 308)
- How do you evaluate an Integral? (Ex 5 pg 308)

__Area Connection__

- How do we interpret the word "area"? (paragraph above Ex 6 pg 308)
- How do you find total area analytically? (pg 309)
- How do you find area using antiderivatives? (Ex 6 pg 308)
- How is the absolute value function used with area? (pg 309)
- How do you find total area numerically? (pg 309)
- How do you find total area using NINT? (Ex 7 pg 309)

__Analyzing Antiderivatives Graphically__

- How can you analyze antiderivatives graphically? (Ex 8 pg 309 - 310 and the text above the example)

**STEP 3: Reading**

__Read__the following page(s) and take any extra notes as needed.

- Read pages 302 - 310.
- Make sure to read the paragraphs between the examples and sidebar snippets.