7.8 Integration Techniques
Improper Integrals: Overview
So far all the integr∫ls ( ) assumed that ( ) was defined and continuous over [ ].
But there are integrals whose interval is infinity, or has infinite discontinuity like vertical asymptotes
caught over . These are called improper integrals.
There are two types of improper integrals:
1) Infinite Intervals
These are where ( ) has thin tails, so that
∫ ( ) ∫ ( ) for every where the limit exists to be a finite number.
( ) ( )
Likewise,∫ ∫ , where the limit exists to be a finite number.
They are called convergent if the limit exists, and divergent if the limit does not exist. If both
infinite ends are convergent, the∫: ( )