Section 6.2 - Definite Integrals

Essential Question(s): 

Explain what a definite integral is and how it is used.

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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 
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.

Riemann Sums

1. What is a Riemann Sum? (pg 281 - 282)
2. What is the definite integral as a limit of Riemann Sums? (pg 283)
3. What is the existence of definite integrals? (pg 283 Theorem)
4. What is the definite integral of a continuous function on [a,b]? (pg 283)

Terminology and Notation of Integration

1. Read about how the notation evolved and came to be. (pg 283 - 284)
2. What are the components of an integral and how is it read? (pg 284 diagram)
3. How do you use the integral notation in place of summation notation? (Ex 1 pg 284-285)

Definite Integral and Area

1. ​​What is the definition of the area under a curve as a definite integral? (pg 285)
2. How do you handle area below the x-axis? (pg 286 paragraphs and graphics in side margin)

Constant Functions

1. ​​What is the integral of a constant? (pg 287 and graphics in side margin)

Definite Integral as an Accumulator Function

1. ​​What is an accumulator function? (pg 288)
   

Integrals on a Calculator

1. Review how the book will denote numerical integrals on the calculator. (pg 289)
2. Look over your calculator and figure out how to do a numerical integral.

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

• Read pages 281 - 290.
• Make sure to read the paragraphs between the examples and sidebar snippets.