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.
Options
Pages: 1
Back to forum
Please log in to reply to this topic or to report it.
Members in this topic: None.
[02:41 am]
Oh_Man -- i used to play TF2 competitive in that clan, and also was PR manager (ie: i wrote all the website posts)[02:39 am]
Oh_Man -- i realised all his shit was halluc and i wiped out his measly army of fake hallucs and he called GG - yeah thts wat actually happened damn false memory strikes again[02:38 am]
Oh_Man -- i was zerg, the toss guy did a bunch of hallucinates, and i was like, welp, i guess i'm dead, but i have that mindset of never giving up, so attacked him anyway, then tht was wen[02:38 am]
Oh_Man -- coz i was actually a zerg main, so wat ACTUALLY happened was a complete reverse of this[02:37 am]
Oh_Man -- i found an old comment of mine i actually think the idra thing over-ride my own memory[01:52 am]
NudeRaider -- Oh_ManOh_Man shouted: and i went on to win the tournament, and a pair of steelseries headphones. i even reember how i won the final match - hallucinated a fck-tonne of units and my opponent thought i had way more than he did and GGed
classic
Members Online: Oh_Man, Sie_Sayoka
Oh_Man, Sie_Sayoka