Math 231 - Merit - Mock Exam 1
Trig identities: sin2 x + cos2 x = 1, tan2 x + 1 = sec2 x, sin(2x) = 2 sin x cos x,
cos2 x = 21 (1 + cos(2x)), sin2 x = 12 (1 − cos(2x))
Multiple Choice
5
Z
1. Evaluate the integral
4
x3
√
dx.
x2 − 16
(a) 53
(b) 114
(c) 57
√
(d) 17 3
(e) None of the above
2. The partial fractions decomposition of
(a)
A
x
+
B
x−1
+
C
x2 +3x+12
(b)
A
x
+
B
x−1
+
Cx+D
x2 +3x+12
(c)
A
x
+
B
(x−1)2
+
(d)
A
x
+
B
x−1
C
(x−1)2
+
Cx+D
x2 +3x+12
+
(e) None of the above
Z
3. Evaluate the integral
π
2
π
4
(a)
(b)
(c)
(d)
√
− √2−2
2
√
− √2+2
2
√
1−
√ 2
2
√2
2
(e) None of the above
Dx+E
x2 +3x+12
sec θ
dθ.
tan2 θ
x3 +2x2 −2x+3
x(x−1)2 (x2 +3x+12)
is
4. The partial fractions decomposition of
(a)
A
x2 −3
(b)
Ax+B
x2 −3
(c)
A
x−3
+
B
(x−3)2
(d)
A
x−3
+
Bx+C
(x−3)2
(e) None of the above
Z
5. Evaluate the integral
e
∞
1
x2 −3
is
1
dx.
x(ln x)2
(a) ∞
(b) 1
(c) -1
(d)
1
e
(e) None of the above
Z
6. Evaluate the integral sin7 x cos3 x dx.
(a)
cos8 x
8
(b) −
sin8
cos10 x
10
−
x
8
+
(c)
sin8 x
8
−
(d)
x8
8
x10
10
−
sin10
10
sin10 x
10
+C
x
+C
+C
+C
(e) None of the above
Free Response
Z
7. Evaluate the integral
Z
8. Evaluate the integral
Z
9. Evaluate the integral
ex sin(2x) dx.
x2 sin2 x dx.
√
x2
x
dx.
+ 2x − 3
x4 + 9x2 + x + 9
10. Evaluate the integral
dx.
x3 + 9x
Z ∞
x−1
√
11. Determine whether the integral
dx converges or diverges.
3
x +5 x+5
1
Z