Math 166
Summer 2002
Exam 1
- (45 pt)Evaluate the
following integrals:
a) b) c)
d) e)
- (15 pt) (Scaling a
function) Find a value of so that the
function has average
value equal to 1 on the interval
- (20 pt) Consider the
functions and
a)
Find
the area of the region enclosed by the two curves.
b)
Find
the volume obtained when the part of this region on the right side of the axis is revolved about the line
- (10 pt) A cylindrical
tank of height with a circular base of radius (both measured
in feet) is filled with a fluid that is pounds per cubic foot. Find the work done in pumping the
fluid out of the tank.
- (10 pt) Suppose that
you have a solid object and you compute the volume using decreasing
cross-sectional areas from the base to height You find that you get the formula How tall is the
object? (Hint: find so that the
cross-sectional area is 0).
- (10 pt) Find the volume
obtained when the region in the first quadrant bounded by and is revolved about the axis. What happens to your answer as What happens to
your answer as What should
happen?