Due date: Thursday 1/29, 11:59pm
Partial fractions
01
01
Link to originalDistinct linear factors
Compute the integral:
Solution
Solutions - 0060-01
(1) Write the partial fractions general form equation:
(2) Solve for constants.
Cross multiply:
Plug in
, obtain so . Plug in
, obtain so .
(3) Integrate each term:
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02
02
Link to originalLong division first
Compute the integral:
Solution
Solutions - 0060-02
(1) Numerator degree is not smaller! Long division first:
Now this already has the form of a partial fraction decomposition, so we proceed directly to integration.
(2) Integrate using power rule (with log):
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03
03
Link to originalRepeated factor
Compute the integral:
Solution
Solutions - 0060-03
(1) Write the partial fractions general form equation:
(2) Solve for constants.
Cross multiply:
Plug in
, obtain . Plug in
, obtain . Plug in
, obtain:
(3) Integrate each term:
Optional simplification:
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Simpson’s Rule
04
01
Link to originalSimpson’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
Solutions - 0070-01
(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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