8.4 day one. Improper Integrals. Greg Kelly, Hanford High School, Richland, Washington. Sometimes we can find integrals for functions where the function or the limits are infinite. These are called improper integrals .
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Greg Kelly, Hanford High School, Richland, Washington
Until now we have been finding integrals of continuous functions over closed intervals.
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.
(right hand limit)
We approach the limit from inside the interval.
This integral diverges.
If then b has a negative exponent and ,
therefore the integral converges.
(P is a constant.)
What happens here?