# Determining Constants of Integration (UMAP)

### Author: Ross L. Finney

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. INTRODUCTION2. INDEFINITE INTEGRALS3. INTEGRALS OF LINEAR COMBINATIONS OF FUNCTIONS4. FRACTIONAL EXPONENTS AND NEGATIVE EXPONENTS5. DIFFERENTIATE TO CHECK6. NUMERICAL CONDITIONS THAT DETERMINE A CONSTANT OF INTEGRATION7. GRAPHICAL CONDITIONS THAT DETERMINE A CONSTANT OF INTEGRATION8. MODELING: INITIAL CONDITIONS FROM PLAUSIBLE ASSUMPTIONS9. REPEATED INTEGRATION10. ANSWERS TO EXERCISES**

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