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Math Help - Inserting Limits Into Integral Result

  1. #1
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    Inserting Limits Into Integral Result

    What would this give: \left[\frac{\cos n\pi t}{n \pi}\right]^0_{-1}.

    The solution given is (1 + \cos n\pi).

    I don't understand what to do with the n\pi because \cos(0) = 1 but what does \cos n\pi (0) equal?
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  2. #2
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    What is your question?.

    cos(n{\pi})=-1 for odd values of n

    cos(n{\pi})=1 for even values of n.

    Is that what you meant?.
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  3. #3
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    Quote Originally Posted by galactus View Post
    What is your question?.

    cos(n{\pi})=-1 for odd values of n

    cos(n{\pi})=1 for even values of n.

    Is that what you meant?.
    I had integral of:

    \int^0_{-1} (1+t)\cos n \pi t \ \mathrm{d}t Through which I used integration by parts and got a similar result to \left[\frac{\cos n\pi t}{n \pi}\right]^0_{-1}.

    The correct is \left[-\frac{\cos n\pi t}{n \pi}\right]^0_{-1} but what would I get if I put the limits in?
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  4. #4
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    \int_{-1}^{0} (1+t)cos(n{\pi}t)dt

    The result should be:

    \frac{1-cos(n\pi)}{(n{\pi})^{2}}
    Last edited by galactus; January 10th 2009 at 02:03 PM. Reason: wrong integral
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