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:
  1. Understand integration as the reverse process to differentiation.
  2. Manipulate differentials sufficiently well to set up integrals.
  3. Solve simple indefinite integrals and separable differential equations.
  4. Solve for initial conditions.
  5. Understand the geometric meaning of the definite integral.
  6. Calculate definite integrals via the Fundamental Theorem of Calculus.

Suggested Procedures:

  1. Read Simmons Chapters 5 and 6.
  2. 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.
  3. Take the Practice Test, Xdvi or PDF.
  4. Ask your instructor to give you a unit test.
The Independent Path page | The Calculus page The World Web Math Categories Page
watko@mit.edu
Last modified August 1, 1998