Why Is Int|4sin(x) + sin(10x)| dx > Int|4sin(x)|dx ?
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From: David C. Ullrich on 13 Aug 2010 08:53 On Sat, 7 Aug 2010 08:37:16 -0700 (PDT), Bret Cahill <BretCahill(a)peoplepc.com> wrote: > >> >> >Is there a list of identities on integrals of absolute values of sums >> >> >of trig functions somewhere? >> >> >> Saying Int|4sin(x) + sin(10x)| dx > Int|4sin(x)|dx is meaningless. >> >> >It seems to be true, at least if the ">" is replaced with ">=." >> >> It can't be true because it's meaningless! Both integrals are >> only _defined_ up to addition of an arbitrary constant; > >You were supposed to assume they are definite integrals over the the >same x interval. You're not paying much attention. If we're given only that they're integrals over the same interval then it's obviously not (necessarily) true that Int|4sin(x) + sin(10x)| dx > Int|4sin(x)|dx . I mean duh. Consider an interval I such that|4sin(x) + sin(10x)| <|4sin(x)| for every x in I. > >. . . > >> >Increase the high frequency term's amplitude a little and the >> >difference between the two functions increases a lot. >> >> >> Where does the question come from? >> >> >Same as any math proof, i.e., why does a^2 + b^2 = c^2? >> >> Huh? I asked where you got the question from. > >No way! You're not getting any account numbers either. > > >Bret Cahill > |