MAC 2312

Review Sheet, Exam 2
October 28, 2008

When: November 5, in class, starting at 3:20

New Material: Sections 7.4, 8.1-8.8

Old Material: Area between curves and volumes of revolution are still fair game.  And of course, you need to be able to do antiderivatives, u-subs, derivatives, precalculus...

Procedure: The test will be closed book.  You will have the entire class period for the test.  One page (8 1/2 by 11 in, front and back) of notes will be allowed.

Suggested Review: Same as last time. Be able to do all of the homework problems without any help from a book or person.  Problems will be "similar" to homework and quiz problems.  I have a liberal view on just how "similar" is defined.  Try to understand the concepts well enough to deal with a problem that doesn't look exactly like one you've done before.  

• Arclength and Surface Area: These boil down to a formula.  I give you a function, an interval, and a task, and you plug it into the correct formula.  Now fortunately for you, there are very few functions that I can give you, because most functions will give you an integral that you cannot evaluate.  You do, however, have all these new integration techniques at your disposal...  Practice Problems: 7.4, 3-12, 39-44, 51-55.
  
• Integration Techniques - General: You really should practice integration outside of the specific sections.  On the test, I will not tell you which technique to use.  Unfortunately, the book doesn’t have many problems where you are not told the technique.  General Practice Problems: page 589, 1-46.
  
• Integration by Table: I will provide you with enough of the table to do any problem that requires it.  Your task will be to fit your integral into one of the forms (perhaps by a u-substitution), and decide which form to use.  You will be allowed to use tables ONLY on problems where I say you can use tables.  For all others, the ONLY integration forms you may assume are on page 364 and Theorem 8.2 on page 547.  Practice Problems: 8.6, 19-50.
  
• Integration by Parts: Next to u-substitution, this is the most important integration rule out there. Make sure you know how to select a good choice for u and a good choice for v (the book lists the general guidelines on page 493).  Also, make sure you know the tabular method, and know when to use it. Practice Problems: 8.2, 11-36, 47-64.
  
• Trigonometric Methods: Multiple sines, cosines, tangents, and secants.  Make sure you know the proper technique, depending on whether the powers are even or odd.  Also included are the trig substitutions.  Make sure you know the proper substitution to make, depending on what's underneath the square root.  Practice Problems: 8.3, 5-18, 25-42; 8.4, 21-38.
• Partial Fractions: Be able to decompose any fraction given to you. Make sure you can also do long division on improper fractions. Practice Problems: 8.5, 7-28.
  
• L’Hopital’s Rule: You will be given limits, and you will evaluate them.  Use L’Hopital’s rule when appropriate, and do not use the rule when it is not appropriate.  Practice Problems: 8.7, 11-50.
• Improper Integrals: Be able to integrate integrals with infinite limits, or functions that are infinite at one of the end points. This basically requires you to be OK with the infinities, and to be able to take limits as things go off to infinity.  Practice Problems: 8.8, 1-32, 67-70.