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MATH 212 OL – PRACTICE #2
Directions: Answer each of the following in the space provided. Please include sketches.
Each problem has equal weight.
1. Find the area of the region bounded by the graphs of the algebraic functions.
f (x) = -x3 + 3
y=x
x = -1
x=1 2. Find the volume of the solid generated by revolving the region bounded by the graphs of
y = x3 and y =
in the first quadrant about the given lines:
x (a) x-axis (b) y -axis 3. Use the shell method to set up and evaluate the integral that gives the volume of the solid
generated by revolving the plane region bounded by y = 0.5 x2 + 1, x = 0 and y = 4 about
the y-axis. 4. Use the disk or shell method to find the volume of the solid generated by revolving the
region bounded by the graphs of the equations y = x3, y = 0 and x = 1 about x-axis. 5. Find the arc length of the graph of the function y = x 3/2 over the interval [1, 8]. 6. Set up and evaluate the definite integral for the area of the surface formed by revolving
the graph of
where 0 < x < 3 about the x-axis.
1 3
y x
3

Attachments:

• 1492745188-PRACTICE 2.docx