anonymous
  • anonymous
\[\int\limits 5 (\sin5\theta) (\sin \theta) d \theta\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Loser66
  • Loser66
take integral by part twice, you get the original problem at both sides. Then, just stay them in one side, calculate the rest.
anonymous
  • anonymous
somehow i got 1/40 sin 4theta - 1/60 sin 6theta. says im wrong
Loser66
  • Loser66
I don't know, you should show your work to be checked.

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zepdrix
  • zepdrix
|dw:1377999712652:dw|
zepdrix
  • zepdrix
Doing it by parts once gave me that. If you took a different method it might not look the same though :o
anonymous
  • anonymous
ok
zepdrix
  • zepdrix
|dw:1378000136136:dw|You'll want your next `By parts` to be line this. The `u` needs to match up with the `theta` function while the `dv` needs to match up with the `5theta` function, because that's how we did it the first time. If you did it the other way, you would find it ends up `undoing` the integration you performed the first time, sending you back to the start. D:
anonymous
  • anonymous
this is where i get lost
zepdrix
  • zepdrix
Too much stuff to keep track of? :)
anonymous
  • anonymous
the second integration confuses me
zepdrix
  • zepdrix
\[\Large u=\cos \theta \qquad\to\qquad du=-\sin \theta\]\[\Large dv=\cos5\theta \qquad\to\qquad v=\frac{1}{5}\sin5\theta\]
anonymous
  • anonymous
I have sin theta (-cos 5theta) + 1/5 sin 5theta sin theta d theta
zepdrix
  • zepdrix
I dont understand, where is the integral?
anonymous
  • anonymous
that is where i got lost. i removed it when i did 1/5
zepdrix
  • zepdrix
So from here: \[\Large -\sin \theta \cos5\theta+\int\limits \cos5\theta \cos \theta \;d \theta\] Applying integration by parts again, with the u and dv I listed above:
zepdrix
  • zepdrix
\[\large -\sin \theta \cos5\theta+\frac{1}{5}\sin5\theta \cos \theta-\int\limits \frac{1}{5}\sin5\theta(-\sin \theta)\;d \theta\]
zepdrix
  • zepdrix
Integration by Parts is so difficult to explain to someone with typing lol :( I wish I had a big big chalkboard i could show you the steps with.
anonymous
  • anonymous
that would be nice
anonymous
  • anonymous
Integration by parts isn't necessary here (but it's always a good idea to practice), if you know the right identities. The angle sum/difference identities for cosine are \[(1)~~~\cos(x+ y)=\cos x\cos y- \sin x \sin y\\ (2)~~~\cos (x-y)=\cos x\cos y+\sin x\sin y\] Note how subtracting (1) from (2) yields \[\cos(x-y)-\cos(x+y)=2\sin x\sin y\] For this particular integral, \(x=\theta\) and \(y=5\theta\).
anonymous
  • anonymous
somehow i got 5/40 sin4theta - 5/60 sin6theta + c as a final answer
anonymous
  • anonymous
says im wrong
anonymous
  • anonymous
Your coefficients are off. Should be 15/24 for sin4 and 10/24 for sin6
anonymous
  • anonymous
oh... i see. thank you
anonymous
  • anonymous
haha still says im wrong. unless im typing it in wrong

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