Oct22.pdf - Improper Integrals Part 2 The second type of...

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Improper Integrals: Part 2The second type of improper integral: the interval is finite, but theintegrand is discontinuous at some points.Iffis continuous on [a,b) and is discontinuous atb, thenZbaf(x)dx:=limtb-Ztaf(x)dx.If the limit exists as a finite number, we say this improper integralconverges, otherwise we say it diverges.Chapter 7.8: Improper Integral,Section 7.8 Improper Integrals13 / 28
Improper Integrals: Part 2Iffis continuous on (a,b] and is discontinuous ata, thenZbaf(x)dx:=limta+Zbtf(x)dx.If the limit exists as a finite number, we say this improper integralconverges, otherwise we say it diverges.Chapter 7.8: Improper Integral,Section 7.8 Improper Integrals14 / 28
Improper Integrals: Part 2Example 1. Find the area under the curvey=1xfor 0<x1.
Chapter 7.8: Improper Integral,Section 7.8 Improper Integrals15 / 28
Improper Integrals: Part 2Solution: By definition,Z101xdx:=limt

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