# math 242: Calculus and Analytic Geometry II (4)

Course Prerequisites/Corequisites: Prerequisite: MATH 241.

Course Description::Definite and indefinite integrals, techniques of integration, transcendental functions, and applications of the definite integral. Four hours of lecture per week.
Listed as MATH 2414 in the Texas Common Course Numbering System.

Textbook: Calculus: Early Transcendentals. Sullivan and Miranda, W.H. Freemand and Company

Course topics

• 4.8 Review Antiderivative.CHAPTER 5
• 5.1 Area
• 5.2 The Definite Integral
• (5.3) The Fundamental Theorem of Calculus
• (5.4) Properties of the Definite Integral
• (5.5) The Indefinite Integral; Growth and Decay Models
• (5.6) Method of Substitution; Newtwon’s Law of Cooling

CHAPTER 6

• (6.1) Area Between Graphs
• (6.2) Volume of a Solid of Revolution: Disks and Washes
• (6.3) Volume of a Solid of Revolution: Cylindrical Shells
• (6.4) Volume of a Solid: Slicing Method
• (6.5) Arc Length
• (6.6) Work
• (6.7) Hydrostatic Pressure and Force
• (6.8) Center of Mass; Centroid: Pappus Theorem

CHAPTER 7

• (7.1) Integration by Parts
• (7.2) Integrals Containing Trigonometric functions
• (7.3) Integration by trigonometric Substitution: integrands containing
$\sqrt{a^2-x^2},\sqrt{x^2+a^2}, \sqrt{x^2-a^2} ,a>0$.
• (7.4) Substitution: integrands contains $a x^2 + bx +C$
• (7.5) Integration of rational functions using partial fractions
• (7.6) Integration Using Numerical Techniques
• (7.8) Improper Integrals

CHAPTER 9

• (9.1) Parametric Equations
• (9.2) Tangent Lines; Arc Length
• (9.3) Surface Area of a solid of Revolution
• (9.4) Polar Coordinates
• (9.5) Polar Equations; Parametric Equations; Arc Length of Polar Equations