Engineering Math II – Spring 2015
Name:
Quiz #1
Section: 561 / 562 / 563
Directions. Read each problem carefully and work it out on a separate sheet of paper.
Put a box around the answer you believe best answers the question. Turn in your work
with this sheet of paper stapled on top.
R4
x
Problem 1 (5 pts). After an appropriate substitution, the integral −1 (x+7)
3 dx is equivalent to which of the following?
R 11
(a) 6 (7u−3 − u−2 )du
R 11
(b) 6 (u−2 − 7u−3 )du
R4
(c) −1 (u−2 − 7u−3 )du
R4
(d) −1 xu−3 du
(e) None of the above
Problem 2 (5 pts). Use the trigonometric
identity 2 sin A cos B = sin(A+B)+sin(A−B)
R
to evaluate the indefinite integral sin 3t cos 2tdt.
(a) − cos5 5t − cos t + C
(b)
cos 5t
5
+ sin t + C
(c)
cos 5t
10
+
sin t
2
+C
(d) − sin105t −
sin t
2
+C
(e) − cos105t −
cos t
2
+C
MATH 152:561-563 – Spring 2015
Problem 3 (5 pts).
(a)
1
4
(b)
sec θ
4θ+ln | sec θ+tan θ|
sec θ tan θ
dθ
4+sec θ
R
=
ln | cos θ| + C
+C
(c) ln |4 + sec θ| + C
(d) ln |4 + tan θ| + C
(e)
1
4
ln | sec θ| + C
Problem 4 (5 pts).
R
cos2 (2x)dx =
(a)
1
x
2
+ 41 sin(2x) + C
(b)
1
x
2
+ 81 sin(4x) + C
(c)
1
x
2
− 81 sin(4x) + C
(d)
1
x
2
− 41 sin(2x) + C
(e)
sin3 (2x)
3
+C
Quiz #1
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