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Integral - help needed please

  1. Jan 27, 2006 #1
    I have been asked to explain without evaluating the integrals why the integral of x cos x from 0 to pi/2 is positive and the integral of x cos x from pi/2 to pi is negative. Also would I expect x cos x from 0 to pi to be positive, zero or negative??? And why ???

    How can I do this without evaluting it??? :frown: some help would be much appreciated, thanks!
  2. jcsd
  3. Jan 27, 2006 #2


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    Do you know what the graphs look like? Keep in mind that a positive function times a negative function is negative, etc, and the integral of a positive function is positive, etc.
  4. Jan 27, 2006 #3


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    If [tex]f(x)\geq 0[/tex] for x in [a,b], then [tex]\int_{a}^{b}f(x)dx \geq 0[/tex].
  5. Jan 27, 2006 #4


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    Do not double-post, please.
    Haven't you got enough information on this page (you posted it 3 days ago remember?)? If you have any further questions, why don't consider to post it there, instead of starting a brand new thread??? :grumpy: :grumpy: :grumpy:
    This proves that some never read the hints in the posts others have given, and think about it, instead, they are looking for a complete solution!!!
    Last edited: Jan 27, 2006
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