Unit 4

Prereq Test 4

Intro

• Integration is an important process of calculus that is closely related to differentiation.

• There are methods and rules for solving definite and indefinite integrals, including the Fundamental Theorem of Calculus.

Overview 4

Inquiry Activity 4

Key Terms

Unit 4 Podcast (coming soon)

4.1 Indefinite Integrals

4.1.1 Antiderivatives of Algebraic Functions

• • Notation

  • Basic Rules

  • Long Division

  • Completing the Square

4.1.2 Antiderivatives of Transcendental Functions

4.1.3 Antidifferentiation by Substitution

4.1.4 Integration by Parts**

4.1.5 Integration using Partial Fractions**

4.1.6 Integration of Vector-Valued Functions**

4.2 Differential Equations

4.2.1 Separable Differential Equations

• • Verifying Solutions

  • Finding General Solutions Using Separation of Variables

  • Particular Solutions using Initial Conditions

4.2.2 Slope Fields*

• • Sketching Slope Fields

  • Reasoning with Slope Fields

4.2.3 Euler's Method**

• • Approximating Solutions

4.3 Definite Integrals and Accumulation of Change

4.3.1 Riemann Sums*

• • Summation Notation

4.3.2 Fundamental Theorem of Calculus

• • Accumulation Functions

  • Connecting Area to Accumulation Functions

4.3.3 Definite Integrals

• • Properties

4.3.4 Improper Integrals**

4.3.5 Area of a Polar Region**