MATH 101 Quiz #4 (v.M3)
Last Name:
Friday, March 4
First Name:
Student-No:
Grade:
Section:
Very short answer question
1. 1 mark Write out the general form of the partial-fractions decomposition of
x3 + 3
.
(x2 − 1)2 (x2 + 1)
You need not determine the values of any of the coefficients.
Short answer questions—you must show your work
Z
1
1
dx is convergent or divergent. If it
10/9
0 (1 − 2x)
is convergent, find its value. Show all your work.
2. 2 marks Determine whether the integral
3. 2 marks Express the x–coordinate of the centroid of the triangle with vertices (−1, −3),
(−1, 3), and (0, 0) in terms of a definite integral. Do not evaluate the integral.
Long answer question—you must show your work
Z
4. 5 marks Evaluate
1
1
dx. A “calculator-ready” answer is acceptable, but your
(1 + 9x2 )3/2
answer may not contain inverse trigonometric functions.
0