Name
ID
MATH 172
Section 502
Multiple Choice: (9 points each)
1. ;
2
0
a.
b.
c.
d.
e.
EXAM 2
Fall 1999
1-7
/63
8
/15
9
/15
10
/15
P. Yasskin
x dx 4 " x2
".
" ln 4
0
ln 4
.
. 2x
dx x3
2
a. ".
b. 3
4
c. 1
d. 2
e. .
2. ;
3. If it requires 12 lb of force to stretch a spring from rest to 3 ft, how much work will it take
to stretch it from 3 ft to 6 ft?
a. 12 ft-lb
b. 18 ft-lb
c. 36 ft-lb
d. 54 ft-lb
e. 72 ft-lb
1
4. The curve y 1 x 3 for 0 t x t 1 is rotated about the x-axis. Find the integral which
3
gives the area of the surface swept out.
1
a. ; 2= 1 x 3 1 x 4 dx
b. ;
0
1
0
1
3
1 x 4 dx
c. ; 2=x 1 x 4 dx
0
1
d. ; 1 x 3 1 x 4 dx
0
1
3
e. ; x 1 x 4 dx
0
5. Given the partial fraction expansion
x 3 dx.
xŸx 1 2
a. 3 ln 2 6 ln 3 1
3
b. 3 ln 2 " 3 ln 3 2
3
c. 6 ln 2 " 3 ln 3 " 1
3
d. 10 ln 2 " 7 ln 3
e. 10 ln 2 " 7 ln 3 " 1
2
;
2
2
x3 3 " 3 "
, compute
x
2
x1
xŸx 1 2
Ÿx 1 1
2
6. Use the Trapezoid Rule with n 3 to approximate ;
a.
b.
c.
d.
e.
9
0
9
10
9 " ln 2 " ln 5
37
24
33
16
37
8
x dx.
x3
7. The function xŸt Ae 5t 3 satisfies which equation?
a. dx 3x " 5
5
dt
b. dx 5x 3
dt
dx
5x " 3
c.
dt
d. dx "5x " 3
dt
e. dx "3x " 5
dt
3
8. (15 points) A square pyramid with the point at the bottom is 10 cm high and the square
at the top is 5 cm on a side. If the pyramid is filled with water, how much work does it
take to pump the water out the top?
> 1 gm3
g 980 cm2
sec
cm
4
2
4.
9. (15 points) Find the partial fraction expansion for 3x " 10x 2
xŸx " 2 5
10. (15 points) Solve the initial value problem
dy
sin2x with yŸ0 3.
dx
y
6