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Math Help - Integration of trig functions

  1. #1
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    Integration of trig functions

    Ok so here is my integral:

    INTEGRAL of [sin(5x)][cos(6x)]dx

    Now this is a pretty simple u-substitution problem, i know that. Except i have one problem. The 5x and 6x inside the two trig functions is throwing me off. Is there a way to pull them apart so i just have a whole bunch of sin(x)'s and cos(x)'s? I'm stumped.
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  2. #2
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    Use the product to sum identity:

    \sin{a}\cos{b} = \frac{1}{2}(\sin{(a+b)} + \sin{(a-b)})

    Then you'll get a simpler integral.
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  3. #3
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    Wow that was quick, thanks a lot. Is there a website with the list of common identities? I got through highschool calc never once talking about identities, and i get to college finding my life is useless without them.
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  4. #4
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    Quote Originally Posted by fogel1497 View Post
    Wow that was quick, thanks a lot. Is there a website with the list of common identities? I got through highschool calc never once talking about identities, and i get to college finding my life is useless without them.
    No problem.

    Visual Calculus - Trigonometric Identities
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  5. #5
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    For my answer I got:

    -.5[ (1/11)cos(11x) + cos(-x)]

    Can anyone confirm this for me?

    My work is as follows:

    INTEGRAL of: Sin5x * Cos6x = 1/2 * INTEGRAL of: sin(11x)+sin(-x)
    by virtue of the Product sum identity

    Which simplifies to -.5[ (1/11)cos(11x) + cos(-x)]
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  6. #6
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    Quote Originally Posted by fogel1497 View Post
    For my answer I got:

    -.5[ (1/11)cos(11x) + cos(-x)]

    Can anyone confirm this for me?

    My work is as follows:

    INTEGRAL of: Sin5x * Cos6x = 1/2 * INTEGRAL of: sin(11x)+sin(-x)
    by virtue of the Product sum identity

    Which simplifies to -.5[ (1/11)cos(11x) + cos(-x)]
    \sin{-x} = -\sin{x}

    \cos{-x} = \cos{x}

    You are right.
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  7. #7
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    Hello,
    Quote Originally Posted by fogel1497 View Post
    Wow that was quick, thanks a lot. Is there a website with the list of common identities? I got through highschool calc never once talking about identities, and i get to college finding my life is useless without them.
    Here is a website I like much : Trigonometry

    The is for the integral sign.

    Enjoy
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