Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Calculus I
Topic: Antiderivatives
Subtopic: Antiderivatives & Indefinite Integrals

Overview

Differentiating takes a function to its derivative. Antidifferentiating reverses this process taking a derivative back to its original function. The result is an antiderivative. The process of finding an antiderivative is called integrating. As differentiating is the major focus of Calculus I, integrating is the major focus of Calculus II, but introduced in Calc I.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 4.1.1 Properly use mathematical notation for antiderivatives and integrals
• 4.1.2 Know how to "read" an integral properly
• 4.1.3 Know when to include the arbitrary constant "+C" and remember to do so consistently
• 4.1.4 Find an antiderivative of a polynomial or power function
• 4.1.5 MEMORIZE the antiderivatives of e^x, 1/x, cos(x), sin(x), sec^2x, csc^2x, sec(x)tan(x), csc(x)cot(x)
• 4.1.6 Find an antiderivative of a function that requires minor simplifying first to rewrite it as a polynomial function
• 4.1.7 Find an antiderivative of a function that first requires minor simplifying via trigonometric identities
• 4.1.7 Solve a very basic differential equation where initial conditions are given

Terminology

Terms you should be able to define: antiderivative, integral, integral sign, arbitrary constant, differential equation (DE), initial condition

Mini-Lectures and Examples

Supplemental Resources (optional)

rev. 2020-11-27