Engineering Math II – Spring 2015
Name:
Quiz #2
Section: 561 / 562 / 563
Directions. Read each problem carefully and work it out on a separate sheet of paper.
Put a box around the choice you believe best answers the question. Turn in your work
with this sheet of paper stapled on top.
Problem 1 (5 pts). The base of a solid is the parabolic region between the graphs of
y = 1 and y = x2 . Cross sections perpendicular to the y-axis are squares. Find the
volume of the solid.
(a)
4
3
(b) 2
(c) 1
(d)
1
3
(e) 3
Problem 2 (5 pts). Find the volume of the solid formed by rotating the region bounded
by x = 0, y = ln(x), y = 0, and y = 2 about the y-axis.
(a)
π 4
e
2
(b)
π 4
e
2
−1
(c) πe4 − 1
(d)
π
2
(e)
π 4
(e
2
− 1)
MATH 152:561-563 – Spring 2015
Quiz #2
2
Problem 3 (5 pts). Which of the following represents the area between the curves y =
and y = 6 on the interval from x = 1 to x = 4?
R4
−
6
dx
(a) 1 12
x
(b)
R2
(c)
R4
(d)
R 12 12
(e)
R6
1
1
6−
12
x
6−
12
x
y
3
3
dx +
R 4 12
2
x
12
x
− 6 dx
dx
− 1 dy
4−
12
y
dy +
R 12 12
6
y
− 1 dy
Problem 4 (5 pts). Find the area of the region bounded by y = cos(x), y = −1, x = 0
and x = π2 .
(a) π
(b)
π
2
(c) 1 +
π
2
(d) −1 +
(e)
π
2
+2
π
2