7.1b: Integration by Parts (Definite Integrals)

Objectives:

• Calculate definite integrals using integration by parts.

Read:

• pgs. 456 - 457

Definitions & Formulas:

• Integration by Parts formula for definite integrals.

Flashcards:

• Integration by Parts formula for definite integrals.

Examples:

Ex1. Using IBP for Definite Integrals (with substitution)

Student example


7.1b problem set:
#19, 20, 23, 24

7.1a: Integration by Parts (indefinite integrals)

Objectives:

• Define Integration by Parts

• Apply integration by parts in finding general indefinite integrals.

Read:

• pgs. 453-456

Definitions & Formulas:

• Integration by Parts Formulas 1 & 2

Flashcards:

• Integration by Parts Formulas 1 & 2

Examples:

A quick explanation of integration by parts.


Ex1. Applying integration by parts

Student example


Ex2. More integration by parts.

Student example


7.1a problem set:
# 1, 6, 9, 15, 29, 34, 38, 40

5.5b: The Substitution Rule for Definite Integrals

Objectives:
Apply the substitution rule when evaluating definite integrals.

Read:
pgs. 403 (starting at "Definite Integrals") - 406

Definitions & Formulas:
The Substitution Rule for Definite Integrals
Integrals of Symmetric Functions

Flashcards:
N/A

Examples:

Ex1. Evaluting definite integrals using the substitution rule.

Student example


Ex2. Evaluating definite integrals using symmetry.

Student example


5.5b Problem Set:
# 53, 58, 66, 69, 73, 78, 82

5.5a: The Substitution Rule (with indefinite integrals)

Objectives:

• Apply a u substitution to find the indefinite integral of a composition of functions.

Read:

• pg. 400 - 403 (through example 6)

Definitions & Formulas:

• The Substitution Rule

Flashcards:
N/A

Examples:

Ex1. Using "u - substitution" (with differentials)

Student Example


Ex2. More complex u - substitution

Student Example


5.5a Problem Set:
# 2, 5, 10, 16, 23, 28, 42, 47

5.4: Indefinite Integrals

Objectives:

• Find antiderivatives of given functions.

• Find specific antiderivatives given initial conditions.

Read:

• pgs. 391-396

Definitions& Formulas:

• Indefinite integral

• Net Change Theorem

Flashcards:

• Everything in the table of indefinite integrals (pg. 392)

• Net Change Theorem

Examples:

Ex1. Evaluating an indefinite integral

Student example


Explanation of Net Change Theorem


Ex2. Applying the Net Change Theorem
(in class)

Problem Set 5.4:

2, 7, 10, 12, 18, 19, 21, 24, 29, 37, 42, 47, 52, 59, 65

5.3b: The Fundamental Theorem of Calculus Part II (FTC II)

Objectives:

• Define and apply the FTC II in evaluating definite integrals.

Read:

• pg. 384 - 387

Definitions:

• The Fundamental Theorem of Calculus Part II (FTC II)

• Differentiation and Integration as inverse processes

Formulas:
N/A

Flashcards:

• The Fundamental Theorem of Calculus Part II (FTC II)

Examples:

A short explanation of FTC II


Ex1. Evaluating a definite integral

Student example


Ex2. Finding the area under a curve

Student example


5.3b Practice Set:
#19, 22, 30, 32, 44, 51, 52

5.3a: The Fundamental Theorem of Calculus (Part I)

Objectives:

• Define FTC I
• Apply FTC I in finding derivatives of "accumulation functions".

Read:

• pg. 379 - 384 (through example 4)

Definitions:

• The Fundamental Theorem of Calculus Part I (FTC I)

Formulas:N/A

Flashcards:

• FTC I

Examples:

A proof(ish) of FTC I


Ex1. Applying FTC I

Student example


Ex2. Finding the Derivative of an accumulation function

Student Example


Ex3. FTC I with the Chain Rule

Student Example


Practice Set 5.3a:
# 3, 6a, 8, 9, 14, 17, 58