MAT270 Final Exam Review
Fall 2013
This is in no way a complete list of topics covered in class, but merely a compilation of the
types of exercises commonly encountered.
1. See Exam 1 review sheet.
2. See Exam 2 review sheet.
3. See Exam 3 review sheet.
Z 4
Z
4. Suppose that
f (x) dx = 6,
1
4
Z
g(x) dx = 4, and
1
4
f (x) dx = 2. Evaluate the
3
followingZintegrals, or state that there is not enough information.
4
(3f (x) − 2g(x)) dx
a.
1
Z
1
(f (x) − g(x)) dx
b.
3
Z
c.
4
f (x)g(x) dx
1
5. State the Fundamental Theorem of Calculus
6. Evaluate the following with the the Fundamental Theorem of Calculus.
Z 2
d x
(sin(θ) + cos(θ)) dθ
a.
dt x
Z b
d
arctan(z) + ln(2z )
b.
dz
dx x3
z 4/21
7. Evaluate the following integrals. Some of them may require a u-substitution to
solve. Z
2
1
a.
(8x5 − 2 + ) dx
x
Z−41
1
√
b.
dx
81 − 9x2
0
Z π/2
c.
cos(θ) dθ
Z0
d.
η 9 (3η 1/3 + 27) dη
1
2
Z
e.
sec(3x) tan(3x) dx
Z
cos(3µ) − cos3 (3µ) dµ
f.
Z
2
37x − 18y dz
g.
1