5.2a: The Definite Integral

Read:
 pg 366 - 372 (Through the Midpoint Rule)


Defintions:

• Definition of a definite integral (also called Riemann sum)
• Theorem 3
• Theroem 4

Formulas:

•  Sigma Formulas (7 of them on pg. 369)
• The Midpoint Rule

Flashcards:

• Theorem 4
• Front: Integral
• Back: Sigma notation / delta x and x_i
•  The Midpoint Rule

Examples:

Ex1.  Expressing a Riemann sum as an integral

Student example *there is a mistake in the final answer, see the comments below for the correction*

Ex2a. Evaluating Riemann sums

Student Example

Ex2b. Evaluating integrals using Theorem 4 and the Sigma Properties

Student Example

Ex3. Evaluating integrals by interpreting areas.

Student Example

Ex4. The Midpoint Rule

Student Example



Practice Problems:
5.2a #1, 6, 8, 9, 18, 23, 26, 33, 36