Chapter 8 Techniques of Integration

Preview For Chapter 7

Techniques of Integration

In Calculus 1, integration was limited to a single substitution and reversing a derivative formula. In Chapter 8 we integrate far more complex integrands involving multiple substitutions.

A student completing this chapter successfully will be able to:

	Integrate algebraically with four techniques: Integration by parts, trigonometric integrals, trigonometric substitution and partial fractions decomposition.
	Integrate using integral tables
	Integrate using a computer algebra system.
	Integrate numerically using Simpson's rule.
	Use limits to determine whether improper integrals converge or diverge..

Calculus 2 Lesson 7.1 Integration by Parts
The following topic is the most important. Typical exercises from Calculus,7th Edition-Early Transcendentals, by James Stewart, are assigned at the end of the objective. In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective.

1.	Integrate by parts. P468#3,5, 7,15,27,33,37(Let z=x^1/2.),53
Maple Assignment: See Maple Assignment Submitting Maple Assignments for a Grade

Calculus 2 Lesson 7.2 Trigonometric Integrals
The following topic is the most important. Typical exercises from Calculus,7th Edition-Early Transcendentals, by James Stewart, are assigned at the end of the objective. In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective.

1.		Integrate trigonometric integrals. P476#1,5,9,25,29,57
		There are several "poems" to help us remember the combinations of trigonometric integrals: SEcant Even Easy! Sine, Cosine or Tangent Odd, Not Hard! (Do they call this poetic license?) Tangent Even, Secant Odd, Very, Very Hard!!! These poems are illustrated in the exercises above as well as the Maple Session below.
Maple Assignment: See Maple Assignment

Calculus 2 Lesson 7.3 Trigonometric Substitution
The following topic is the most important. Typical exercises from Calculus,7th Edition-Early Transcendentals, by James Stewart, are assigned at the end of the objective. In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective.

1.	Integrate using trigonometric substitution. P483#1,2,3,5,7,11,15,23
Maple Assignment: See Maple Assignment

Calculus 2 Lesson 7.4 Partial Fractions Decomposition
The following topic is the most important. Typical exercises from Calculus,7th Edition-Early Transcendentals, by James Stewart, are assigned at the end of the objective. In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective.

1.	Integrate rational functions using partial fractions decomposition. P492#1-17 odd, 39, 45, 47
Maple Assignment: See Maple Assignment

Calculus 2 Lesson 7.5 Strategy for Integration
The following topic is the most important. Typical exercises from Calculus,7th Edition-Early Transcendentals, by James Stewart, are assigned at the end of the objective. In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective.

1.	Integrate. P499#1-35 odd
Maple Assignment: none

Calculus 2 Lesson 7.6 Integration Tables and Computer Algebra Systems
The following topic is the most important. Typical exercises from Calculus,7th Edition-Early Transcendentals, by James Stewart, are assigned at the end of the objective. In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective.

1.	Integrate using integral tables. P504#1,5,9,13,21
2.	Integrate using a computer algebra system (Maple). P505#37,39
Graphing Calculator Hints show how to evaluate derivatives and definite integrals using the TI-86.
Maple Assignment: none

Calculus 2 Lesson 7.7 Approximate Integration
The following topic is the most important. Typical exercises from Calculus, 6^th edition, by James Stewart, are assigned at the end of the objective. In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective.

1.	Use a graph, table or formula of a function with the Midpoint rule, Trapeziodal rule and Simpson's rule to find the approximate value of its definite integral (M_n, T_n, and S_n) P516#7,33,35
2.	Estimate the error E_M, E_T, and E_S for a given definite integral and value of n. P516#19,25
Maple Assignment: See Maple Assignment

Calculus 2 Lesson 7.8 Improper Integrals
The following topic is the most important. Typical exercises from Calculus,7th Edition-Early Transcendentals, by James Stewart, are assigned at the end of the objective. In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective.

1.	Determine whether improper integrals having infinite limits of integration converge and if so to what value. P527#5,7,9,13,17
2.	Determine whether improper integrals with discontinuous integrands converge and if so to what value. P527#27,29,35,39
Maple Assignment: See Maple Assignment