Trying to find the area between two sine waves, f(x) = 11.6164sin(0.85x-4.99)+23.8656, and 8.2264sin(0.883x-4.77)+17.3568, basically what do I do next to evaluate the infinite series?
My text book is shaky at best.
None.
Alright, I'm nearly done this piece of crappy calculus, but I have no idea how to properly evaluate definite integrals because even though the homework I'm doing requires it... We haven't done it in class yet?
Trying to find the area between two sine waves, f(x) = 11.6164sin(0.85x-4.99)+23.8656, and 8.2264sin(0.883x-4.77)+17.3568, basically what do I do next to evaluate the infinite series?
My text book is shaky at best.
Trying to find the area between two sine waves, f(x) = 11.6164sin(0.85x-4.99)+23.8656, and 8.2264sin(0.883x-4.77)+17.3568, basically what do I do next to evaluate the infinite series?
My text book is shaky at best.
Um i'm not sure exactly what you're asking for... could be that I forgot all my calculus/series from like forever ago.
I'm assuming you would just find the area (solve the anti derivative) with the limits 9 and 0 whereas normally when solving indefinite integrals you add the "+ C" at the end to indicate an unknown constant (and sometimes you would have to solve for this value of C.)
∫^9_0 ( 11.6164 * sin( 0.85x - 4.99 ) + 23.8656 )dx - ∫^9_0 ( 8.2264 * sin(0.883x - 4.77) + 17.3568 )dx
= ∫^9_0 (11.6164 * sin( 0.85x - 4.99 ))dx + ∫^9_0 (23.8656)dx - ∫^9_0 (8.2264 * sin(0.883x - 4.77))dx - ∫^9_0 (17.3568)dx
= -11.6164 * cos(0.85x - 4.99) / 0.85 |^9_0 + 23.8656x |^9_0 + 8.2264 * cos(0.883x - 4.77) / 0.883 |^9_0 - 17.3568x |^9_0
= -13.67cos(0.85x - 4.99) + 9.32cos(0.883x - 4.77) + 6.51x |^9_0
= -13.67cos(0.85*9 - 4.99) + 9.32cos(0.883*9 - 4.77) + 6.51*9 - (-13.67cos(0 - 4.99) + 9.32cos(0 - 4.77) + 0)
= 64.6
someone may have to verify and make sure I made no errors...
I'm assuming you would just find the area (solve the anti derivative) with the limits 9 and 0 whereas normally when solving indefinite integrals you add the "+ C" at the end to indicate an unknown constant (and sometimes you would have to solve for this value of C.)
∫^9_0 ( 11.6164 * sin( 0.85x - 4.99 ) + 23.8656 )dx - ∫^9_0 ( 8.2264 * sin(0.883x - 4.77) + 17.3568 )dx
= ∫^9_0 (11.6164 * sin( 0.85x - 4.99 ))dx + ∫^9_0 (23.8656)dx - ∫^9_0 (8.2264 * sin(0.883x - 4.77))dx - ∫^9_0 (17.3568)dx
= -11.6164 * cos(0.85x - 4.99) / 0.85 |^9_0 + 23.8656x |^9_0 + 8.2264 * cos(0.883x - 4.77) / 0.883 |^9_0 - 17.3568x |^9_0
= -13.67cos(0.85x - 4.99) + 9.32cos(0.883x - 4.77) + 6.51x |^9_0
= -13.67cos(0.85*9 - 4.99) + 9.32cos(0.883*9 - 4.77) + 6.51*9 - (-13.67cos(0 - 4.99) + 9.32cos(0 - 4.77) + 0)
= 64.6
someone may have to verify and make sure I made no errors...
None.
I don't ever remember having to try to evaluate infinite Riemann sums without an integral, and I'm not sure how to go about it without proving the Fundamental Theorem..
the integral though is
[-13.666cos(0.85x-4.99) + 23.8656x 0|9 - [-9.313cos(0.883x-4.77) + 17.3568x 0|9
= [-13.666cos(0.85x-4.99) + 9.313cos(0.883x-4.77) + 6.5088x 0|9
Oh, if MA does the numbers I'll check it, one sec.
Yes, 64.593 (with the 3-digits-past standard)
where f(x) a|b denotes f(b) - f(a)
Post has been edited 1 time(s), last time on Mar 9 2009, 2:44 am by DT_Battlekruser.
the integral though is
[-13.666cos(0.85x-4.99) + 23.8656x 0|9 - [-9.313cos(0.883x-4.77) + 17.3568x 0|9
= [-13.666cos(0.85x-4.99) + 9.313cos(0.883x-4.77) + 6.5088x 0|9
Oh, if MA does the numbers I'll check it, one sec.
Yes, 64.593 (with the 3-digits-past standard)
where f(x) a|b denotes f(b) - f(a)
Post has been edited 1 time(s), last time on Mar 9 2009, 2:44 am by DT_Battlekruser.
None.
Crap, I accidently was using the wrong equations anyways XD Thanks anyways, I should be able to do it now.
None.
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Oh_Man -- No APM in chess. Computer just outthinks the human by seeing more moves ahead and more permutations[05:47 pm]
NimoStar -- If its any consolation, the human brain would still mop the floor with this bot if it wasn't limited by the mechanical interface[05:34 pm]
NimoStar -- Well. The bot didn't come up with any new strategy. It just has superhuman micro. Hard to beat that. I reckon even the simplest dedicated chess engines are unbeatable for humans now.[10:54 am]
NudeRaider -- Oh_ManOh_Man shouted: NudeRaider did u watch the entire video? it's not one game. it's currently dominating the ladder at number 1 position. do ur research first!
Oops, caught me there, no I haven't. 
I was imagining how the game went. Sorry for that. Watching it now. brb[10:52 am]
NudeRaider -- NimoStarNimoStar shouted: They were not "Unprepared" that was their fifth loss in a row against the bot. The other replays are also available
that doesn't mean he was prepared. When humans come around with new strategies it often takes weeks until the pros figure out how to shut it down. Oh_ManOh_Man shouted: https://youtu.be/GiQ-cDtsZYw
that's certainly a way more convincing argument for micro being "too good to beat".[08:35 am]
NimoStar -- " its shown is that you can trade 1000's of apm to make up for lack of strategy"
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