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600-232 CALCULUS II
SAMPLE GATEWAY TEST #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:
- The area under the graph of f
- The arclength of the graph of f
- The volume of S.
- The surface area of S.
- (20 points) Sketch the region bounded by the curves
y = x2 + 6x and y = 3x - 2, and find its area.
- (20 points) A solid sits on the (x,y)-plane, with its
base bounded by the curves y = -x2, y = 3x2,
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?
- (10 points) Suppose that a force moves an object along the
x-axis from x=1 to x=e2. If the force at any point on the
axis is given by , find the work done by
- (10 points) Find the average value of the function
f(x) = 2x2 + 3 on the interval [0, 1].
Kevin B Mcleod