Thursday, September 30, 2010

Problem Solving Hints - Stick With It!

During my Calculus II class on Wednesday, we were working an example with integration by partial fractions.  We had broken down the integral into three different integrals.  The one that I did not know how to do is below.

The nasty integral.

We worked on it in class on Thursday, and used Maxima to find the antiderivative.  However, at the time I was not able find out how to do it by hand.  So the students, one other faculty member, and I worked on it off and on for two days.  Today, we finally found the solution.

To find the solution, it took an integration table and one differential equation to set up the integration by parts.  I do not believe that a normal Calculus II student could have found the answer, which is why I could not find it worked out in either of the calculus texts I used as a reference.

The moral of the story is:
  1. Stick with a problem until it is finished.
  2. Do not be satisfied with an answer that technology gives you.  You do not learn anything by letting the computer do the work for you.
  3. Do not be afraid to use the tools available to you.  You should learn to do the problem by hand, but books and technology can get you started in the right direction.
  4. Learn to work and talk math with other people.  It is a valuable skill because very few people can survive learning math alone.
P.S.  I am not sharing the answer.  You will have to work it out for yourself.