SMA 200 • CALCULUS 2

Objectives of the Lesson Meaning of Integration Constant of Integration The Notation Basic Formula for Integration of Functions Addition and Subtraction Rule in Integration Integration of Constant Times a Function

Objective of the Lesson Definition of Integrand The Extension of the Basic Formulae Proof of the Extension Formulae

Objectives of the Lesson Integration using Substitutions Type I Type II Type III Integrand containing u and u’ in other forms, (eu u1, sin u u

Objectives of the Lesson Formulae for Integration by Parts Formula for Integration of ln x

Objectives of the Lesson Review of important Trigonometric identities Integration using the three fundamental identities Integration using the formulae for cos 2 x Integration using the product formulae Integration using sin 3 x and cos 3 x formulae Integrand containing quadratic expressions in the Denominator

Objectives of the Lesson Integrand Containing only non-repeated linear Factors in th Integrand Containing linear Factors (non-repeated) in the Den Integrand Containing Quadratic Factors Integrand is an (Improper Fraction)

Objectives of the Lesson Meaning of the Definite Integral Important Properties of Definite Integral Definition of Indefinite Integral The Fundamental Theorem of the Integral Calculus Evaluation of Definite Integrals

Objectives of the Lesson Formula for the Area under a Curve Area Below x – axis Combined Area under a Curve Area Between Two Intersecting Curves

Objectives of the Lesson Definition of Improper Integrals Convergence and Divergence of the Improper Integrals of the F Definition of Absolute and Conditional Convergence Cauchy’s Inequality for convergence of an Integral Absolute Convergence of an Integral Implies Convergence Convergence and Divergence of the Improper Integrals of the S The Cauchy’s Principal value of Improper Integrals with Singu

Objectives of the Lesson Length of the Arc in Cartesian Form Length of the Arc in Parametric Form Length of the Arc in Polar Coordinates

Objectives of the Lesson The Formula for the Volume of Solids of Revolution The Formula for the Surface Area of Solids of Revolution

Objectives of the Lesson Area of a Trapezium Trapezoidal Rule Principle of Simpson’s Rule Simpsons Rule Objectives of the chapter state the Ten Basic Formulae for integration. integrate simple functions using the Ten Basic Formulae only. Meaning of Integration