4. Integration.....................................................................................................................................
IndefiniteIntegralsCalculus
LearningObjectives
A studentwill be able to:
- Find antiderivativesof functions.
- Representantiderivatives.
- Interpretthe constantof integrationgraphically.
- Solvedifferentialequations.
- Use basicantidifferentiationtechniques.
- Use basicintegrationrules.
Introduction
In this lessonwe will introducethe idea of the antiderivative of a functionand formalizeas indefinite
integrals. We will derivea set of rulesthat will aid our computationsas we solveproblems.
Antiderivatives
Definition: A function is calledanantiderivative of a function if for all in the
domainof
Example1:
Considerthe function Can you think of a function such that ?(Answer:
manyotherexamples.)
Sincewe differentiate to get we see that will workfor any constant
Graphically, we can think the set of all antiderivativesas verticaltransformationsof the graphof
The figureshowstwo suchtransformations.