Calculus
Lesson
47
Improper
Integrals
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Integrals can be "improper" in two different ways:
1) One or more of the limits is evaluated at infinity.
YOU MUST convert, the first thing you do, to get rid of the infinity!
You evaluate at infinity since infinity is not an integer.
Examples: 
2) If there is an infinite discontinuity within the limits on the integral
Don't forget to check inside as well!! 
Special form to memorize: 
Examples: 
Find the volume and surface area of 
rotated about x-axis.
(Special form, p=2)
since the square root is always > 1
so each rectangle has a larger height
than one with 1/x, and we know
that the special form with p=1
always diverges anyway!