Integration Gateways
Math 2205
In Math 2205 one of your exams is the Integration Gateway. It is essentially worth 10%
of your final course grade: fail and your course grade drops by one grade point. Starting
Spring 2008, gateways are administered with the online tool WebWork.
Each Gateway has 7 questions. 6 correct is passing. There is no partial credit. You have
5 weeks to pass the Gateway in a computer environment. Like a driving test, you may
take this exam repeatedly, but no more than once a day. Gateways will be available in
the Math Lab (Ross Hall Room 27), and twice a week in the computer lab, Engineering
2106. You are allowed 45 minutes to complete the 7 questions. NO calculator or notes
on a Gateway. The proctor will not wait for you to finish if you arrived with fewer than 45
minutes left in the session. Scratch paper is provided. Bring only a photo ID and pencils.
Practice exams!
You have access to online practice exams through WebWork. The practice exams are
built from the same pool of problems as the proctored exams, and also allow only 45
minutes to finish. In fact, we hope you’ll have passed a practice exam before you take a
proctored exam. Space is limited and it’s not fair to others when you use the proctored
exams for your practicing. Anyone can signup for a Guest gateway:
http://webwork.math.uwyo.edu/
Once assigned by your instructor, a link appears on your WebWork homepage: Take
New PracticeIntegralGW test. Your exam is stored so that you and your instructor can
review your work. Each time you attempt an exam, a new version is generated. If you
use the Guest login, the exam is anonymous and your instructor won’t see it.
Skills Covered
 WebWork will do the result simplification. For example, you may write ln 8  ln 2
instead of simplifying to ln 4 . You may type a trig expression such as cos 12 and
let WebWork evaluate.

You will also need to know the 5 identities below:
1
1  cos 2x  
2
1
cos 2 x   1  cos 2x  
2
M
ln x  M ln x 
sin 2 x  
 


x   1  cos x sin x 
cos 3 x   1  sin 2 x  cos x 
sin 3



2
Know integration “facts” like those on page 369 in our textbook, Calculus Concepts
and Contexts (3rd Ed) by James Stewart.
Know how to combine the standard facts with range of problems suitable for
substitutions. Most problems require some sort of substitution, perhaps two.
Know the parts method applied to products involving first or second powers, trig
functions, exponentials or logs. There is only one question that requires this
technique.
Suggestions
1. Take practice exams to pinpoint your problem areas. Work with a group of other
students.
2. Know how to express a logarithm or a root in WebWork.
3. Go to your instructor's office hours, and bring your worked practice exams and
reworked exams that you have tried to pass during the semester.
4. Go to the Math Lab (basement Ross Hall 27) and ask for specific help on the topics
you've had trouble with. Show the proctor your past exams.
5. Work an exam twice before hitting the submit button. Work out all the answers on
scratch paper.
6. Check your typing! Hit the Preview Answer key.
7. Check your answers! Differentiating your antiderivatives checks whether they are in
fact antiderivatives.
8. Keep trying! Don't give up - some pass the Gateway on their first try and others may
take it multiple times before passing.