Chapter 8 Techniques of Integration

Preview For Chapter 8
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.
We integrate algebraically with four techniques:
	Integration by parts,
	Trigonometric integrals,
	Trigonometric substitution, and
	Partial fractions decomposition.
We integrate using integral tables, found inside the back cover of Stewart.
We integrate using a computer algebra system, namely, Maple.
We integrate numerically, adding Simpson's rule to the list of numerical methods which include the trapezoidal and midpoint rules from Chapter 4.
Finally we integrate integrals involving infinity, called improper integrals.

Calculus 2 Lesson 8.1 Integration by Parts
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.	Integrate by parts. P493#3,5, 7,15,27,33(Let z=x^1/2.),53
Maple Assignment: See Maple Assignment Submitting Maple Assignments for a Grade

Calculus 2 Lesson 8.2 Trigonometric Integrals
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.	Integrate trigonometric integrals. P501#1,5,9,25,29,57
Maple Assignment: See Maple Assignment

Calculus 2 Lesson 8.3 Trigonometric Substitution
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.	Integrate using trigonometric substitution. P508#1,3,5,7,11,15,23
Maple Assignment: See Maple Assignment

Calculus 2 Lesson 8.4 Partial Fractions Decomposition
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.	Integrate rational functions using partial fractions decomposition. P517#1-17 odd, 39, 45, 47
Maple Assignment: See Maple Assignment

Calculus 2 Lesson 8.5 Strategy for 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.	Integrate. P524#1-35 odd
Maple Assignment: none

Calculus 2 Lesson 8.6 Integration Tables and Computer Algebra Systems
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.	Integrate using integral tables. P529#1,5,9,37,39
2.	Integrate using a computer algebra system (Maple).
Graphing Calculator Hints show how to evaluate derivatives and definite integrals using the TI-86.
Maple Assignment: none

Calculus 2 Lesson 8.7 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) P541#7,33,35
2.	Estimate the error E_M, E_T, and E_S for a given definite integral and value of n. P541#19,25
Maple Assignment: See Maple Assignment

Calculus 2 Lesson 8.8 Improper Integrals
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.	Determine whether improper integrals having infinite limits of integration converge and if so to what value. P551#5,7,9,13
2.	Determine whether improper integrals with discontinuous integrands converge and if so to what value. P551#27,29,35,41
Maple Assignment: See Maple Assignment