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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