MATH 101 Quiz #4 (v.M1)
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
7x3 + x2 − x − 1
.
(4x2 − 1)2 (x2 + 3)
You need not determine the values of any of the coefficients.
Short answer questions—you must show your work
Z
3
1
dx is convergent or divergent. If it is
6/5
0 (x − 1)
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, −1),
(−1, 1), and (1, 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
2
1
dx. A “calculator-ready” answer is acceptable, but your
(1 + 4x2 )3/2
answer may not contain inverse trigonometric functions.
0