Engineering Math II – Spring 2015
Quiz #5
Name:
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.
Z ∞
sin2 x
Problem 1 (5 pts). Which statement is true about the integral
dx?
x2
1
(a) The integral diverges by oscillation.
(b) The integral converges to 0.
∞
Z
(c) The integral diverges by comparison to
1
1
dx.
x
∞
Z
12 dx.
(d) The integral diverges by comparison to
1
Z
(e) The integral converges by comparison to
1
Z
Problem 2 (5 pts). Evaluate
∞
0
(a) 3
(b) -3
(c) 0
(d) The improper integral diverges.
(e) None of these.
2
6xe−x dx
∞
1
dx.
x2
MATH 152:561-563 – Spring 2015
Quiz #5
2
Z
3
Problem 3 (5 pts). Which statement is true about
0
1
dx?
4x − 2
(a) The integral converges to ln 10 − ln 2.
(b) The integral converges to
1
10
+ 12 .
(c) None of the other statements is true.
(d) The integral diverges.
(e) The integral converges to
1
4
ln 10 − ln 2 .
Z
∞
Problem 4 (5 pts). Which statement is true about
2
dx
?
x + e2x
∞
Z
e2x dx.
(a) The integral diverges by comparison to
2
∞
Z
(b) The integral diverges by comparison to
2
Z
(c) The integral converges by comparison to
2
(d) None of the other statements is true.
(e) The integral converges to 0.
1
dx.
x
∞
e−2x dx.