Midterm 1, Math 30, Fall 2008, 10/6/08
1) Find the volume of a solid when the region bounded by )sin(xy
=
and y=0 is
revolved around the y-axis (10 pts)
2) An enclosure for rare reptiles must maintain an average temperature of 30C. The
temperature profile during the day is given by )
48
cos()( tTtT m
π
= where t is in hours.
Find Tm so that the average temperature during 24 hours is 30C. (10 pts)
Evaluate the following integrals: Answer must be in terms of x
3) ∫−dx
x
x1
2 (10 pts)
4) ∫−+
+dx
x
x
x
6
53
2 (10 pts)
5) A tank with 2000 gal of water is being drained at the rate given in the diagram. How
much water is left in the tank after 50 min ? (12 pts)
Time (min)
gal/min
Drain rate
30
30 60