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

1. What are the two outcomes of the Fundamental Theorem of Calculus? (paragraph above Theorem 4 pg 302)
2. What is the antiderivative part of the Fundamental Theorem of Calculus? (Theorem 4, pg 302)
3. What does the antiderivative part equation of the Fundamental Theorem of Calculus tell us? (pg 303 and text below green box)
4. How do you apply the Fundamental Theorem of Calculus? (Ex 1 pg 303)
5. How do you apply the chain rule with the Fundamental Theorem of Calculus? (Ex 2 pg 304)
6. How do you use the properties of definite integrals and the chain rule with the Fundamental Theorem of Calculus? (Ex 3 pg 304)
7. 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

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

​Fundamental Theorem, Evaluation Part

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

Area Connection

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

Analyzing Antiderivatives Graphically

1. 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.