01
Simpson’s Rule
The chart above shows a record of ambient temperatures measured each 15 minutes over 3 hours. Compute the approximate average temperature using Simpson’s Rule. You may use a calculator to resolve the arithmetic in your final expression.
Solution
04
(1) Recall the formula for the average value of
over : Here
and :
(3) Use
in Simpson’s Rule:
(4) Plug into average value formula:
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02
Simpson’s Rule for volume by shells
Use Simpson’s Rule with
to compute the volume of the solid obtained by revolving the pictured region about the -axis. Can you do it without using a calculator?
Solution
10
(1) Recall shells formula:
(2) Interpret:
Bounded above by
. Bounded below by -axis. Bounded left by
. Bounded right by . Obtain:
(3) Create table of values to apply Simpson’s Rule:
(4) Recall Simpson’s Rule formula:
Here
since in this formula represents the integrand values. Note that
. Plug in:
Therefore:
Therefore:
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03
Area of a garden bed
Solution
11
(1) Set up integration:
Set
at the left upper corner, with extending to the right, extending downwards. Then:
(2) Create table of values:
(3) Recall Simpson’s Rule formula:
Here
and . Thus:
(4) Compute cubic yards from known surface area:
Mulch is
deep, so the volume is: Link to original