60 pts.
Problem 1. In each part, give the form of the partial fraction decomposition.
The answer is a formula involving undetermined coefficients. Do
not find the coefficients! (No calculation is required!!).
A.
B.
C.
40 pts.
x2 + 1
(x − 1)(x + 1)(x − 2)
x3 + x + 1
(x − 2)(x + 1)3
x2 + x + 1
(x + 2)(x2 + 1)
Problem 2. In each part, determine if the improper integral converges or
diverges. If it converges, find the value.
A.
∞
Z
e−5x dx
0
B.
2
Z
0
40 pts.
1
dx
x
Problem 3. Use the method of partial fractions to find the following integral.
Z
3x2 − 2x + 2
dx
x(x2 + 1)
1
100 pts.
Problem 4. In each part, find the integral.
A.
Z
B.
Z
C.
Z
D.
E.
1 1
dx
ln(x) x
x3 ln(x) dx
1
dx.
(9 − x2 )3/2
Z p
Z
4 + x2 dx
1
dx,
x2 + 4x + 13
(irreducible quadratic)
2
EXAM
Exam 2, Version 2
Math 1352, Spring 2010
April 1, 2010
• Write all of your answers on separate sheets of paper.
You can keep the exam questions when you leave.
You may leave when finished.
• You must show enough work to justify your answers.
Unless otherwise instructed,
give exact answers, not
√
approximations (e.g., 2, not 1.414).
• This exam has 4 problems. There are 240 points
total.
Good luck!