MIDTERM 2 REVIEW TOPICS
Review homework, quizzes,
examples from book and lecture examples. Do a couple of sample midterms.
Have all needed formulas & trig. functions special values in your notes.
6.4
Work:
- Be able to set up and
solve problems of all 4 types described in class
- Understand how to use
Riemann sums to set up the integrals for cases C and D
- Spring problems, tank
problems, chain problems
6.5
Average value of a function:
- Know and be able to
apply the formula to find the average value of a continuous function f(x)
over an interval [a,b]
- Understand how it
relates to area under curve
METHODS
OF INTEGRATION:
Know
how and when to apply each of these.
Do
lots of practice problems: examples in book, from class, homework, exercises at
the end of chapter (pages 540-542), or from sample midterms.
7.1
Integration by Parts
7.2
Trig Integrals
- Sin/cos : trig formulas
and strategies for solving integrals
- Sec/tan: trig formulas
and strategies for solving integrals
- Have the integrals of
tan and sec on your list of formulas. Look over some trickier examples.
7.3
Trig Substitution
- Three main patterns: be
familiar with them and when to apply each
- Completing the square:
when is it necessary? How to do it?
7.4
Partial Fractions
- Understand the method
and when it applies.
- Be able to do long
division, and to factor of the denominator
- How to break down into
partial fractions: repeated versus non-repeated factors and linear versus
quadratic factors
- Sometimes you need to do
a substitution first, then PF
7.5
Strategy for Integration: how to choose an optimal method. Guidelines +
practice, practice, practice.
7.7
Approximating Integrals
- Know and be able to apply
correctly the Midpoint Rule, Trapezoidal Rule and Simpson’s Rule
- Problems can involve a
function or a table of data; Sometimes can be combined with a
work/volume/etc problem.
7.8 Improper Integrals
- Understand what makes
an integral proper or improper; be able to identify an integral as
improper and to split it into a sum of improper ones if necessary.
- Recall limits and L’Hospital’s
Rule. (See brief review sheet on the website, on the left-hand sidebar)
- Write each integral as
a limit of a proper integral; compute the proper integral; then compute
the limit of the result
- When does an improper
integral diverge?