Final Exam, Math 30, May 16, 2008
Solve for y explicitly. Indefinite integrals must be in terms of x. Check out useful
information in the Appendix.
1) Find the volume of the solid obtained by rotating the given region about the y-
axis. (10 pts)
Region bounded by: 31),ln(
≤
≤
=xxy
Evaluate the following indefinite integrals (10 pts each) solutions must be in
terms of x.
2) ∫dx
x
x)sin(ln
3) ∫+dx
xx 5
1
22
4) Calculate the constant c for the probability density function p(x) (10 pts)
500)(
50)5()( 2
><=
≤≤−=
xandxxp
xxxcxp
5) Find the solution to the differential equation (15 pts)
2)0(,
65
2=
++
=y
xx
y
dx
dy
6) Air freshener’s (AF) evaporation rate is given by daym
dt
dm /02., =−=
λλ
and
m is the mass. If after 10 days 10.0 mg of AF is left, what was the starting mass of
AF? (10 pts)
7) A climate model for carbon dioxide concentration in atmosphere (C) in ppm is
represented by the following equation.
)350)(400()450( 2CCCk
dt
dC −−−=
a) Find and identify by type all equilibrium points (10 pts)
