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    Image To PDF 20240217 16.08.01

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    Jasvinder Solanki

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    Image To PDF 20240217 16.08.01

    Uploaded by

    Jasvinder Solanki
    7 views1 page

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    Image to PDF 20240217 16.08.01

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    Copyright:

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    7 views1 page

    Image To PDF 20240217 16.08.01

    Uploaded by

    Jasvinder Solanki

    Copyright:

    © All Rights Reserved
    Download as PDF or read online from Scribd
    Download as pdf
    of 1
    4:07 4 App Store < Integrals @ \ \ iy logs) = a si (og) =? S, fora [=== Noi in practice, we normally do not mention he interval over which he various unetions ae define. However in fc problem one has to keep tin min. 12.1 Some properties of indefinite integral In this sub section, we shall derive some properties of indefinite integrals (0) The process of differentiation and integration ae inverses ofeach other in sense of the following resus 4 fpeoae op (2) +, where Cis any arbitary constant a fred Proof Lethe any adnan fi Then Jordearenec 4 aoe trevor — Afyarar= L¢reo40) de = dra=s0) Similarly, we mote that a oye L100) Ky +e andtene fd here Cis abivay constant calle cons oie (1) Two indefinite integrals with the same desivative lead (the same family of curves and so they are equivalent Prva Lt and be two Funston such ht @ a {fpunds = Lfavree @ « — Efpede-feurae]=0 Hence J /6)de—f (dsm Chere Cisany eal mumber (Why?) a fron jeavaree Soe families of curves {f (0) d-+C,-C,< R} and {fe0odr+C,.C€R} ae demic Hence, inthis sense, fs) cand fg) are equivalent [= Note] The equivalence of the fa {Jetae+s€,€R) scusomaniy expresedby wring [/odc= fet dr, a 1s [fsaecGeR) ana

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