Test 1 Review Sheet—Math 122
Spring 2005, Prof. Frank
This exam will cover sections 5.6, 5.7, 6.1, 6.2, 6.4, 7.1, 7.2, and 7.3 (eight total).
General principles to guide your study:
(1) Reread each section in the book, along with your notes for that section and the
comments in the study guide for that section. Make a note of every important fact,
definition, and theorem from that section that you feel you should memorize.
(2) Go over your HW assignments and make sure that you understand all of the problems,
as well as the related problems in the text. Pay close attention to the ones you missed
the first time around.
(3) Think about the questions listed below only after you have completed your review.
Try and figure them out without referring to your notes.
Note: many of the following questions are more vague and open-ended than what will be on
your exam. They are intended as food for thought, to help you explore the concepts.
I will post a list of review sheet hints on my website this weekend. Try the
problems on your own first!!!
(1) Discuss the similarities and differences between Zf(x)dx and Zb
a
f(x)dx.
(2) If F(x) and G(x) are both antiderivatives of f(x), is it correct to say that Zf(x)dx =
F(x) + C=G(x) + C? Why or why not?
(3) True or false? d
dx Zf(x)dx =f(x) + C.
(4) Which of the following integrals equals Z3
1
(x+ 5)3dx? (a) Z3
1
u3du or (b) Z8
6
u3du?
Use the one you’ve chosen and compute the value of the integral.
(5) Here are some fun integrals to try:
(a) Zcos x(cos(sin x))dx
(b) Z(1 + √x)3
√xdx
(c) Zln(ln x)
xln xdx
(6) For each of the following, draw regions bounded by functions f(x) and g(x) between
x= 1 and x= 5 as specified. (Note that you will have four different graphs when you
are done. Note also that you don’t need to write any equations for the functions.)
(a) To compute the area of the region you must divide it into three pieces.
(b) A solid of revolution around the x-axis can be computed using washers.
(c) A solid of revolution around the x-axis can be computed using disks.
(d) A solid of revolution around the x-axis cannot be reasonably created.
