#
Unit 6 : Integration

Up to this point we've been studying differential calculus, dealing
with derivatives. Now we will move on to integral calculus and study
(surprise!) integrals. We will look at integration from two
perspectives: Integration is the reverse operation of differention,
and integration can be used to find the area under a curve.

### Objectives:

After completion of this unit you should be able to:
- Understand integration as the reverse process to
differentiation.
- Manipulate differentials sufficiently well to set up
integrals.
- Solve simple indefinite integrals and separable differential
equations.
- Solve for initial conditions.
- Understand the geometric meaning of the definite integral.
- Calculate definite integrals via the Fundamental Theorem of
Calculus.

### Suggested Procedures:

- Read
*Simmons* Chapters 5 and 6.
- Work problems from from
*Simmons* Sections 5.2-5.5 and
6.3-6.7. As usual, the specific problems
don't matter much, but you need to work enough of these to feel
comfortable with the process of integration. Make sure to do plenty of
problems from 5.3, 5.4, 6.6 and 6.7, as these are the sections that
emphasize problem solving, while the others emphasize concepts.
- Take the
**Practice
Test**, Xdvi or PDF.
- Ask your instructor to give you a unit test.

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watko@mit.edu
Last modified August 1, 1998