#### Consortium for Mathematics and its Applications

Product ID: 99162
Supplementary Print

# 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.

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

UMAP Module
39 pages

Calculus

#### Application Areas:

Physical Sciences , Physics

#### Prerequisites:

If derivative of a function is 0 on an interval then the function is constant on that interval; differentiate and graph polynomial and exponential functions; rules for differentiating sums and multiples of functions