1. Yes, scribe is here, late, but at
least done. Had to look over the
material, as it was already
confusing to me. So, it would be a
little hard to scribe if I don't even
know the material we're doing.
So, let's begin.
Some practice questions.
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2. Consider the rgion P bounded by the graph of the function
f between x = ­8 and x = ­5
f (x) = √(x + 9)
Setup, do not evaluate, the integral that
represents the volume of the solid generated
by revolving P about:
The Y axis
the line x = ­10
the line x = 3
2

3. f (x) = √(x + 9) The Y axis
(Radius) (Height) (Width)
The Width is dx, because
we make the number of
cylinders infinitly small.
The height is the given function
The Radius is ­x, because we need to make the
radius equal to 8 when evaluating from ­8 and 5
from ­5
3

4. f (x) = √(x + 9) the line x = ­10
The Width is dx, because
we make the number of
cylinders infinitly small.
The height is the given function
The Radius is x+10, because we need to make the
radius equal to 2 when evaluating from ­8 and 5
from ­5
4

5. f (x) = √(x + 9) the line x = 3
The Width is dx, because
we make the number of
cylinders infinitly small.
The height is the given function
The Radius is 3­x, because we need to make the
radius equal to 11 when evaluating from ­8 and 8
from ­5
5

6. So, some knowledge that
should be known for the next
slide...
*Goes to Visual Calculus
to see the explanation for
the Average Value of a
function within a given
Interval.*
6

7. So, after doing that... we got that cool formula.
Let's try it out.
f (x) = 1 ­ 2x [0,3]
Plug the values in... and we get...
7

8. Once again, run to visual
calculus (we love this site) and
we find how to obtain the Mean
Value Theorem for Integrals.
8

9. And that should be all. I don't remember getting to the last slide. So,
next scribe is me again (because it's late) and so, the homework is...
8.4 Odds
Cya around!
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