Math 111

Chapter #1 : DEFINITE INTEGRAL

Summation and its properties

Definite Integral

Properties of definite integral

Chapter # 2 : INDEFINITE INTEGRAL

Anti-derivative of a function

The Fundamental Theorem of Calculus

Indefinite Integral

Integration by substitution

Chapter # 3 : LOGARITHMIC AND EXPONENTIAL FUNCTIONS

Natural Logarithmic function

The Natural Exponential function

The general logarithmic and exponential functions

Inverse trigonometric functions

Chapter # 4 : HYPERBOLIC FUNCTIONS AND THEIR INVERSES

Hyperbolic functions

The inverse hyperbolic functions

Chapter # 5 : TECHNIQUES OF INTEGRATION

Integration by Parts

Trigonometric Integrals

Trigonometric Substitutions:

Integrals of Rational Functions

Miscellaneous Substitutions

Chapter # 6 : INDETERMINATE FORMS AND IMPROPER INTEGRALS

Indeterminate forms

Improper Integrals

Chapter # 7 : APPLICATIONS OF DEFINITE INTEGRALS

Area of a plane region

Solid of Revolution

Arc Length

Surface of revolution

Chapter # 8 : POLAR COORDINATES

Polar Coordinates

Relation between polar and Cartesian coordinates

Polar Curves

Area of a region in the polar plane