MATH 111 - INTEGRAL CALCULUS

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