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7.8 Improper Integrals Overview

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7.8 Integration Techniques Improper Integrals: Overview Improper Integrals 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∫: ( )
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