More on solids of revolution; introduction to finding the average value of a function.

1. The Average
Value of a
Function ...
Trigonometry at the Forks

2. Consider the region S bounded between the graphs of the functions
ƒ and g.
Find the volume of the solid generated by revolving S around the x-axis.

3. Consider the region S bounded between the graphs of the
functions ƒ and g.
Find the volume of the solid generated by revolving S around the y-axis.

4. Consider the region S bouded between the graphs of the functions
ƒ and g.
Find the volume of the solid generated by revolving S around the
line x = -3.

5. Consider the region S bounded between the graphs of the
functions ƒ and g.
Find the volume of the solid generated by revolving S around the
line x = 6.

7. Consider the region P bounded by the
graph of the function ƒ between x=-8
and x=-5.
Set up, but do not evaluate, the integral
that represents the volume of the solid
generated by revolving P about:
(a) the y-axis. (b) the line x=-10. (c) the line x=3.

8. Average Value of a Function
Definition: Let f be a function which is continuous on the
closed interval [a, b]. The average value of f from x = a to x = b is
the integral:
An animated discussion ...
Average Value of a Function @ Visual Calculus
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