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Math Help - integration

  1. #1
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    integration

     \int\cos ^ {2004}x\cos 2004x\ dx
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  2. #2
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    Re: integration

    This can be solved using a bunch of integration by parts with a little help by a useful trig identity.

     \int_{a}^{b} u \frac{dv}{dx} dx = \left. uv \right|_{x=a}^{b} - \int_{a}^{b} \frac{du}{dx} v dx

    Let  u = \cos^{2004}{x} \ , \ \frac{dv}{dx} = \cos{2004x} \Rightarrow v = \frac{1}{2004} \sin{2004x}

     \int \cos^{2004}{x} \cos{2004x} dx = C + \frac{2004}{2004} \int \sin^{2003}{x} \sin{2004x} dx

    Continue integrating by parts until you notice a pattern. This pattern should take you all the way down to an integrand that you can split up using a handy trig identity. (One that takes the product of two trig functions and gives the sum of two other trig functions).
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  3. #3
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    Re: integration

    any other way
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  4. #4
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    Re: integration

    Quote Originally Posted by ayushdadhwal View Post
    any other way
    type the equation into a Ti 89 and write what it gives you
    ^^ is probably the best way to do it by hand
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