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    when i integrate cos(2x)cos(5x)

    i obtain the following answer:

    1/14 sin(7x) - 1/6 sin(-3x) + c



    is this the same as the answer in the textbook>>>

    1/14 sin(7x) + 1/6 sin(3x) + c
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    sin(-x)\equiv-sin(x)

    so yes
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    (Original post by FoOtYdUdE)
    when i integrate cos(2x)cos(5x)

    i obtain the following answer:

    1/14 sin(7x) - 1/6 sin(-3x) + c



    is this the same as the answer in the textbook>>>

    1/14 sin(7x) + 1/6 sin(3x) + c
    It is, but for what reason? What is \sin (-x) equal to, i.e. is it an odd or even function?
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    (Original post by Pheylan)
    sin(-x)\equiv-sin(x)

    so yes
    so my original answer's not wrong?
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    (Original post by FoOtYdUdE)
    so my original answer's not wrong?
    Your answer was correct, but do you understand why? It is because sin(x) is an odd function.
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    (Original post by TheNack)
    Your answer was correct, but do you understand why? It is because sin(x) is an odd function.
    sinx is an odd function? huh? cuz it contains an odd number??? so an even function = sin(4x) etc?? sin(99x) = odd function?
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    (Original post by FoOtYdUdE)
    sinx is an odd function? huh? cuz it contains an odd number??? so an even function = sin(4x) etc?? sin(99x) = odd function?
    A function f is even if f(x) = f(-x) and odd if -f(x) = f(-x)

    So f(x) = x^2 is even but f(x) = sin(x) is odd.
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    (Original post by TheUnbeliever)
    A function f is even if f(x) = f(-x) and odd if -f(x) = f(-x)
    have you made a typo?
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    (Original post by FoOtYdUdE)
    have you made a typo?
    No?
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    (Original post by TheUnbeliever)
    No?
    erm. nvm i dint undastand wt u wrote tho. thnx anyway.
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    (Original post by FoOtYdUdE)
    erm. nvm i dint undastand wt u wrote tho. thnx anyway.
    He's trying to make sure you understand WHY they are same, as you seem happy just to accept they are.

    The reason is that sin(x) is an odd function, where an odd function is defined as f(-x) = -f(x). So sin(-x) = -sin(x) as it is odd.

    In your case, - 1/6 sin(-3x) is equal to 1/6sin[-(-3x)] which is 1/6 sin(3x).

    You need to understand why they're the same for similar questions.
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    If I were you, I would ignore the odd/even terminology. You simply need to remember that sin(-x) is identical to -sin(x). If you take a look at a graph of y=sin(x) it should be pretty straightforward to see why, but don't get worked up over the reasoning. As long as you know that it is true, you'll be fine.
 
 
 
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