Math 1210-001
Homework 8
Due 17 July, 2013
This homework assignment is designed to go along with sections 4.1 through
4.2 of your textbook, which we have completed in class. Make sure your work
is neat, legible, well-organized and self-explanatory. You must staple your
assignment to receive full credit.
Name:
1. (10 points) In the song The Twelve Days of Christmas, my true love gave me 1 gift on
the first day, 1 + 2 gifts on the second day, 1 + 2 + 3 gifts on the third day and so on for
12 days.
(a) Find the total number of gifts given in 12 days.
(b) Find a simple formula for Tn , the total number of gifts given during a Christmas of
n days. (Your final answer may not use “Σ” or “. . .”.)
2. (10 points) Find the area of the region under the curve y = 12 x2 + 2 over the interval
[−2, 2]. To do this, divide the interval into n equal subintervals, calculate the area of the
corresponding circumscribed polygon and then take the limit as n approaches ∞. (See
the example from class.)
3. (10 points) Use Interval
Z 5 Additivity and the appropriate area formulas from planar gef (x)dx if
ometry to calculate
0
√
2

 1−x
f (x) = x − 2


3
if 0 ≤ x ≤ 1
if 1 < x < 3 .
if 3 ≤ x ≤ 5
No credit will be given for answers that use information from beyond §4.2.
4. (10 points) Calculate the Riemann sum for f (x) = − x2 + 3 on the interval [−3, 2] using
the partition
P : −3 < −1.3 < 0 < 0.9 < 2; x1 = −2, x2 = −0.5, x3 = 0, x4 = 2