MATH 2414 Lecture 4: MATH 2414 Lecture 4
5 Oct 2018
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7g dx area between curve t x axis fcx. 2 if fbfaddx exists for all of ceb then fix dx bfcxjdx faddx exist for some real number a then fcxjdx and f fcxdx t ja fix dx. In all 3 cases the integral divergent if it doesnot. F dx dx fifa f ct fifa f is convergent if the limit exists or. A divergent xexdx. fiofoxexdx fiioscxexii siexdx fiioslxex e"ii a x du i l eet et. If d dx fi of xdx fiiosfarctanxjf fiisarctan0 aretant. It dx findcantanx finstan t tan o iz. Integral type2 discontinuities f is continuous on a b and discontinues at b then. 2 if f is continuous bfcxdx ha fbfcxdx on cab and discontinuous at a then. 3 if f has a discontinuity at c a clb and both affixdx and bfcxdx exists then faddx1 bfcx1dx bfaddx. In all 3 cases the integral is convergent if the limit exists or divergent if it doesnot.
