MATH 1451 Exam 2

Our second exam will be Wed, Mar 7 in class.
The exam will cover material since the first exam.
In particular, this is sections 7.5, 7.6, 7.7, 8.1,
8.2, 8.3, 8.4, and 8.5.

There will NOT be questions on error behavior in 7.5 (those
are the sections headed "Error in ..."), Simpson's rule
in 7.5, known cross-sections from 8.2, arc length of
parametric curves in 8.2, slope or arc length in polar
coordinates from 8.3.

Remember that one of the best ways to prepare for the test
is to work on practice problems.  These might include
problems from the Suggested Study Problems (on the class
website), odd-numbered problems from text (which have
answers available on WileyPLUS in the "Read, Study &
Practice" section), problems in the WileyPLUS assignments.
Don't just read the problems and solutions - copy the problem
to a new sheet of paper and try to work out the answer
yourself.

To help organize your studying, I've listed some of the
major topics from this material:

- Numerical methods of integration(LEFT, RIGHT, MID, TRAP)

- Improper integrals with infinite limits

- Improper integrals with infinite integrads

- Comparison of integrals to determine convergence or divergence
   (incl. good functions like 1/x^p and e^{-a x} as given in
    the "Useful Integrals for Comparison" box in section 7.7)

- Areas by slicing

- Volumes by slicing

- Volumes of solids of revolution

- Arc length

- Graphing and Area in polar coordinates

- Finding a total quantity given a density function (section 8.4)

- Finding total mass of a 1-dimensional rod, 2-dimensional region,
   or 3-dimensional solid given a mass density function

- Find the center of mass with point masses, a rod with given
   mass density function, or a 2D region with constant density.

- Compute total work done by a variable force (like compressing
   a spring or pulling up a heavy chain).  You should be able
   to work with both British units like foot-pound and
   metric (SI) units like joules.

- Compute the force of water pressure against a 2D object.