MATH UN1102 Lecture Notes - Lecture 10: Improper Integral, If And Only If, Direct Comparison Test
4 Jan 2020
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Two types : type 1 : attend x type 2 : lab hxldx. Definition lat tf fat hxldx exists for all tza then f! The improper integrals are convergent if the limit exists. Hxldx and fad full dx exists and converge , then i ! F ! tlxldxtfaflxldx ( doesn"t depend on a) Q : why not fin. f ! tundx ? not convergent. O - in htt ) limit does not exist. = - x ex - f - e xdx = - x ex - e- t (at fxe. = tinti - , exists when - gtfo eff case 2 : p = i times ftdx = t. im in txt it. = thing in itt - o divergent. # dx is convergent if and only if psl. !ft is continuous on la , b ) with id at b , then the improper integral lab hxldx = ftp. atfcxldx (b) if f is continuous on la , b )
