up for test index

**600-232 CALCULUS II
SAMPLE GATEWAY TEST #1**

- 1.
- (10 points each) Let , ,
and let
*S* denote the solid of revolution generated when the
area under the graph of *f* is revolved around the *x*-axis.
Write down and simplify, but do *not* evaluate, integrals
that give the following:
- (a)
- The area under the graph of
*f*
- (b)
- The arclength of the graph of
*f*
- (c)
- The volume of
*S*.
- (d)
- The surface area of
*S*.

- 2.
- (20 points) Sketch the region bounded by the curves
*y* = *x*^{2} + 6*x* and *y* = 3*x* - 2, and find its area.
- 3.
- (20 points) A solid sits on the (
*x*,*y*)-plane, with its
base bounded by the curves *y* = -*x*^{2}, *y* = 3*x*^{2},
*x* = -2 and
*x* = 2. The cross-sections perpendicular to the *x*-axis
are rectangles, whose height is half their base. What is
the volume of the solid?
- 4.
- (10 points) Suppose that a force moves an object along the
*x*-axis from *x*=1 to *x*=*e*^{2}. If the force at any point on the
axis is given by , find the work done by
the force.
- 5.
- (10 points) Find the average value of the function
*f*(*x*) = 2*x*^{2} + 3 on the interval [0, 1].

*Kevin B Mcleod*

*2/18/2002*