INTEGRALS
CHAPTER 1: INDEFINITE INTEGRALS
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1. ANTIDERIVATIVE AND INDEFINITE INTEGRAL
A. DEFINITION OF THE INDEFINITE INTEGRAL
B. PROPERTIES OF THE INDEFINITE INTEGRAL
C. BASIC INTEGRATION FORMULAS
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2. INTEGRATION METHODS
A. INTEGRATION BY SUBSTITUTION
B. INTEGRATION BY PARTS
C. INTEGRATING PARTIAL FRACTIONS
D. INTEGRATING RADICAL FRACTIONS
E. INTEGRATING TRIGONOMETRIC FUNCTIONS
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CHAPTER 2: DEFINITE INTEGRALS
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1. EVALUATING DEFINITE INTEGRALS
A. DEFINITION OF THE DEFINITE INTEGRAL
B. THE FUNDAMENTAL THEOREM OF CALCULUS
C. PROPERTIES OF THE DEFINITE INTEGRAL
D. LEIBNIZ’S RULE
E. THE MEAN VALUE THEOREM
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2. INTEGRALS OF SOME SPECIAL FUNCTIONS (OPTIONAL)
A. INTEGRATING ABSOLUTE VALUE FUNCTIONS
B. INTEGRATING SIGN FUNCTIONS
C. INTEGRATING FLOOR FUNCTIONS
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CHAPTER 3: APPLICATIONS OF DEFINITE INTEGRALS
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1. FINDING THE AREA UNDER A CURVE
2. OTHER APPLICATIONS
A. CALCULATING THE VOLUME OF A SOLID OF REVOLUTION
B. FINDING THE LENGTH OF A CURVE (OPTIONAL)
C. CALCULATING THE AREA OF A SURFACE OF REVOLUTION (OPTIONAL)