Calculus 8.3 day 1

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8.3 day one
Improper Integrals
Greg Kelly, Hanford High School, Richland,
Washington
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Until now we have been finding integrals of
continuous functions over closed intervals.
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Example 1
The function is undefined at x 1 .
Can we find the area under an infinitely high
curve?
Since x 1 is an asymptote, the function has no
maximum.
We could define this integral as
(left hand limit)
We must approach the limit from inside the
interval.
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Rationalize the numerator.
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This integral converges because it approaches a
solution.
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Example 2
(right hand limit)
We approach the limit from inside the interval.
This integral diverges.
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Example 3
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(No Transcript)
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Example 4
What happens here?
(P is a constant.)
p