MAT136H1 Lecture : 7.8 Improper Integrals Overview
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Improper integrals assumed that ( ) was defined and continuous over [ ]. So far all the integrals ( ) But there are integrals whose interval is infinity, or has infinite discontinuity like vertical asymptotes caught over [ ]. There are two types of improper integrals: infinite intervals for every where the limit exists to be a finite number. These are where ( ) has thin tails, so that. If both infinite ends are convergent, then: ( ) number . , where the limit exists to be a finite number. For [ ) where ( ) is discontinuous on , then ( ) ( ) the limit exists. Likewise, for ( ] where ( ) is discontinuous on , then ( ) ( ) given that the limit exists. They are called convergent if the limit exists, and divergent if the limit does not exist. If ( ) is discontinuous on where , then ( ) ( )
