## Section 10.2 - Limits & Motion: The Area Problem

**Essential Question(s):**

Explain how area is used to determine distance traveled from changing velocity.

**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.

__Distance from a Constant Velocity__

- Review computing distance traveled? (Ex 1 & Ex 2 pg 804-805)

__Distance from a Changing Velocity__

- What is used to determine distance from a changing velocity? (pg 805)

__Limits at Infinity__

- What is the informal definition of a limit at infinity? (pg 805)
- Consider the exploration 1. How were limits used? (pg 805-806)

__The Connection to Area__

- How is area used to calculate distance of a velocity function that varies? (pg 806)
- How do you approximate an area with rectangles? (Ex 3 pg 807)
****Make sure to read paragraphs below example****

__The Definite Integral__

- How is a summation used with finding area? (top of pg 808)
- What is a Riemann sum? (left pg 808)
- What is the definite integral? (pg 808) ***big deal***
- How can you use area to compute an integral? (Ex 4 & 5 pg 808-809)
*(read the paragraph prior)*

**STEP 3: Reading**

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

- Read pages 804 - 809.
- Make sure to read the paragraphs between the examples.