MATH 101 Quiz #4 (v.A2)
Last Name:
Friday, March 4
First Name:
Grade:
Student-No:
Section:
Very short answer question
1
3x3 − 2x2 + 9
in the partial fraction expansion of 2
.
x−1
x (x − 1)(x2 − 2x + 3)
Simplify your answer completely.
1. 1 mark Find the coefficient of
Answer:
Short answer questions—you must show your work
Z
2. 2 marks Evaluate
(x2
1
dx.
+ 9)3/2
R1
3. 2 marks The integral −1 cos(x2 ) dx is estimated using the Midpoint Rule with 1000 points.
Show that the error in this approximation is at most 2 · 10−6 in absolute value.
Rb
You may use the fact that when approximating a f (x) dx with the Midpoint Rule using n
points, the absolute value of the error is at most K(b − a)3 /24n2 where |f 00 (x)| ≤ K for all
x ∈ [a, b].
Long answer question—you must show your work
4. 5 marks Find the x-coordinate of the centre of mass of the (infinite) region lying to the right
of the line x = 2, above the x-axis, and below the graph of y = 8/x3 .