Calculus 2
(INTEGRAL CALCULUS)
Table of Contents
TEACHER:
Engr. Herdinio Z. Caneja
Bachelor of Science in Electrical Engineering ( B.S.E.E
)
1.
Introduction
2. The Integration Process:
2.1 Integral of a Function
2.2 General Properties of Indefinite Integrals
2.3 Integration by the General Properties
2.4 Integrals leading to Logarithms
2.5 Integrals of Exponential Functions
2.6 Integrals of Trigonometric Functions
2.7 Integrals Involving Powers of Trigonometric Functions
3. Inverse Functions ; Integration By parts :
3.1 Inverse Trigonometric Functions
3.2 Integrals Leading to Logarithmic Functions
3.3 Integration By Parts
3.4 Hyperbolic Functions
3.1 Inverse Trigonometric Functions
4. Integration by Substitution:
4.1 Introduction
4.2 Algebraic Substitution
4.3 Trigonometric Substitution
5. Integration by Partial Fractions; Constant of Integration:
5.1 Partial Fractions
5.2 Linear Factors
5.3 Repeated Linear Factors
5.4 Quadratic Factors
5.5 Repeated Quadratic Factors
5.6 The Constant of Integration
6. The Definite Integral ; Wallis’ Formula :
6.1 The Definite Integral
6.2 Properties of the the Definite Integral
6.3 Integrals of Even and Odd Functions
6.4 Change of Limits
6.5 Wallis’ Formula
7. Plane Areas :
7.1 Introduction
7.2 The symbol 𝚺
7.3 Differential of Area
7.4 Area by Summation
7.5 The Fundamental Theorem
7.6 Plane Areas in Cartesian Coordinate
7.7 Area Between Curves
7.8 Plane Areas Polar Coordinates
7.9 Parametric Equations
7.10 Improper Integrals