an integration problem

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ian
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an integration problem

Postby ian » Thu Feb 24, 2011 10:09 pm UTC

(homework related)
i'm trying to solve:
[math]\int\sin^2 ({\alpha\pi x}) cos({\beta\pi x}) dx\[/math]
(integral sign) sin^2 (a*pi*x) . cos (b*pi*x) dx

how should i go about this? i've tried integration by parts but it's making it harder not easier. can anyone offer some pointers?

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Talith
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Re: an integration problem

Postby Talith » Thu Feb 24, 2011 10:51 pm UTC

Do you know how to write sin and cos in terms of exponential functions and imaginary numbers? If you don't that's fine, but that's how I'd hit this problem. Also your teacher might not want you to use this approach if you've not seen it before. Just at a glance, I'd think that sin^2=1-cos^2 would be a pretty good way to go here.

[EDIT]another hint which will help if you use the c^2+s^2=1 approach, what trig identity do you know which involves the product of two cosines?[/EDIT]

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ian
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Re: an integration problem

Postby ian » Thu Feb 24, 2011 11:23 pm UTC

yeah expos and i's are fine.

i can get it so i've got a (sin a sin b) integral but changing that to a product of cosines just seems to make things worse

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Talith
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Re: an integration problem

Postby Talith » Thu Feb 24, 2011 11:48 pm UTC

ok you went for putting it in to the sin form, that's fine. There's a nice trig identity for the product of sines aswell, sin(a)sin(b)=1/2(cos(a-b)-cos(a+b)). See if that helps you out.


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