TALLAHASSEE COMMUNITY COLLEGE
MAC 2312-100582 / CALC2 / SUMMER ’11
TEST #02 / §8.1, 8.2, 8.3, 8.4, 8.5 & some of §8.8
THOMAS’ CALC 11-th ed ET.
Instructor D.Jones / DATE of TEST: Mon. 6-13-11
LAST _____________________
FIRST ____________________
INSTRUCTIONS: Do all work & put all answers on your work-sheets. Box your final answer. Do
no more than 3 problems per page. Draw a horizontal line between problems on the same
page. Write on one side only. Draw axes w/ a straightedge. The Bonus problem is 5 points.
Problems #1, 4, 6, and 8 are 9 points each. The remaining problems are 8 points each.
From §8.1.
1.
Evaluate
t
 sec  2  dt
2.
Use a u-subs, evaluate & show work

x dx
x2  1
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
From §8.2.
Use Integration by Parts (IP) & evaluate. (You may use Folley’s Method if you wish
and if it applies).
2
 x sec  x  dx
3.
4.

x 1
x 0
x 2e x dx
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
From §8.3.
5.
Expand the rational function using Partial Fraction Decompositions (PFD). Simplify your
answer. (You may use the Heaviside Cover Up Method (HCOM) if you wish and if it applies.)
2t  3
t  8 t  15
2
6.
Use PFD and evaluate. Give an exact answer. (No calculator result permitted.)

7.
x 1
x 0
3x  2
dx
x  2x  1
2
Same instructions as in #5, above.
x3
x2  2 x  1
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
From §8.4.
8.
Evaluate
9.
Evaluate
Show work. Give Exact Answers. No Calculator results Permitted.


t  2
t 0
x 0
x  
sin 4  t  cos 3  t  dt
sin  3 x  cos  2 x  dx
[See next page for a HINT.]
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
t02_cacl2_100582_20110611sat_s11.docx // page 1 of 2
From §8.5.
Use Trig. substitutions in these two problems.
10. Evaluate

dx
11.
x x2  1

dx
9  x2
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
From §8.8.
12. Evaluate
Show work. Give Exact Answer. No Calculator results Permitted.


t2
3
dt
t2  t
[ See below for a HINT.]
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
Bonus: Use the shell method to find the volume of the solid generated by revolving the region in
the first quadrant bounded by
1
y  x2 , x  2 , and y  0 about the y-axis. The units are inches.
2
Draw a fairly neat sketch. Show work. Set up your integral. Evaluate. Give an exact answer.
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
Hints: (In no particular order.)




b 

lim ln
0
b
 b  1
1
cos   m  n  x   cos   m  n  x  
2
1
sin  mx  cos  nx    sin   m  n  x   sin   m  n  x  
2
1
cos  mx  cos  nx   cos   m  n  x   cos   m  n  x  
2
sin  mx  sin  nx  
t02_cacl2_100582_20110611sat_s11.docx // page 2 of 2