Determining Constants of Integration (UMAP)

A unit that involves calculus and determining constants of integration. With completion of this module students will: 1) know that an indefinite integral is a family of functions having a common derivative; 2) be able to write the indefinite integral of a linear combination of functions whose indefinite integrals are known; 3) be able to determine from an indefinite integral the particular function that satisfies a given initial condition; and 4) be able to determine constants of integration from initial conditions stated in various ways.

Table of Contents:

1. INTRODUCTION

2. INDEFINITE INTEGRALS

3. INTEGRALS OF LINEAR COMBINATIONS OF FUNCTIONS

4. FRACTIONAL EXPONENTS AND NEGATIVE EXPONENTS

5. DIFFERENTIATE TO CHECK

6. NUMERICAL CONDITIONS THAT DETERMINE A CONSTANT OF INTEGRATION

7. GRAPHICAL CONDITIONS THAT DETERMINE A CONSTANT OF INTEGRATION

8. MODELING: INITIAL CONDITIONS FROM PLAUSIBLE ASSUMPTIONS

9. REPEATED INTEGRATION

10. ANSWERS TO EXERCISES