Math 171 — Calculus I Spring 2016
Name:
1
Weekly Write-Up on Sections 5.1-5.2
Problem 1.
From the suggested homework:
Z2
(2 − |x|) dx and compute it
[5.2 #9] Draw a graph of the signed area represented by
−2
using geometry.
Problem 2. From an old exam:
q
2 Z
n
b
X
2 + 1 + ni
If lim
=
f (x)dx.
n→∞
n
a
i=1
Then: a =
,b=
, and f (x) =
.
2
Problem 3.
For in-class discussion:
We want to approximate the volume of the wine bottle shown below. This wine bottle
was chosen because it has an interesting shape that cannot be considered as a solid
of revolution. You will learn techniques to compute volumes of solids of revolution in
M172.
Slicing the bottle parallel to its bottom,
we see that the cross sections are circular. Thus, we can approximate the volume using a section method. The idea is
to break the object up into pieces that we
can compute the volume of.
Each cross section is a circle and the dimensions of the widths of the bottle are given
every 2 centimeters for the bottom 18 centimeters of the bottle in Figure below. Use
this information to estimate the volume of the bottom 18 centimeters of the bottle.
Find an over estimation and an under estimation of the true volume.
2.0 cm
2.0 cm
2.5 cm
4.0 cm
5.5 cm
7.0 cm
7.5 cm
8.0 cm
7.5 cm
5.5 cm
18.0 cm