Name
ID
MATH 172
EXAM 1
Section 502
Fall 1999
1-9
/45
10
/15
11
/15
12
/15
13
/10
14
/10
P. Yasskin
Multiple Choice: (5 points each)
; x x 2 " 1x dx
2x 7/2 2x "3/2 C
3
7
2x 7/2 " 2x 1/2 C
7
2x 37/2 2x "3/2 C
3
3
3
3/2
x
x
" lnx 2x Ÿx 2 " lnx C
3
3
2x 3/2 x 3 " lnx C
3
3
1. Compute:
a.
b.
c.
d.
e.
2. Evaluate
a.
b.
c.
d.
e.
2 2=
1=
1 2=
="1
2=
;
2
0
4 " x 2 1 dx
by interpretating it as an area.
3. Find the area between the parabola y x 2 and the line y 2x 3.
a. " 16
b.
c.
d.
e.
3
16
3
32
3
9
88
3
1
4. Compute
a.
b.
c.
d.
e.
;
4
1
lnx dx
2 x
2 ln 4 " 1
2 ln 4 " 2
2 ln 4 " 4
2 ln 4 " 6
ln 2 " 4
gm
for 0 t x t 3. Find the total
gm
for 0 t x t 3. Find the
5. The mass density of a 3 cm bar is > 1 x 2 cm
mass of the bar.
a. 4 gm
b. 10 gm
c. 12 gm
d. 18 gm
e. 30 gm
6. The mass density of a 3 cm bar is > 1 x 2 cm
x-coordinate of the center of mass of the bar.
a. 3
2
b. 2
c. 7
3
d. 33
16
e. 99
4
2
7. Compute
;
=/2
0
sin 4 2 cos 2 d2
a. " 1
3
b. " 1
c. 1
6
d. 1
5
e. 1
3
5
8. Compute
;
=/4
0
tan 3 2 sec 2 2 d2
a. " 1
b. 1
4
4
c. " 1
d. 1
3
3
e. " 1
2
9. Compute:
2
; x 4 " x 2 dx
0
a.
b.
c.
d.
e.
2 2
3
8
3
24
32
3
6
3
10. (15 points) Compute
1
; Ÿt 2 " t e 2t dt
0
4
x2 " 1
dx
x
1
You must evaluate any inverse trig functions in the answer.
11. (15 points) Compute
;
2
5
12. (15 points) Find the arc length of the parametric curve x 1 t 6 , y t 4 between
t 0 and t 1.
HINT:
Factor the quantity in the square root.
2
6
13. (10 points) Find the volume of the solid whose base is the triangle with vertices Ÿ0, "1 ,
Ÿ1, 0 and Ÿ0, 1 and whose crosssections perpendicular to the x-axis are semicircles.
7
14. (10 points) The area between the parabola y x 2 and the line y x is rotated about
the indicated axis. Find the volume of the solid swept out.
a. x-axis
b. y-axis
8