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Math Help - Calc II - Area btw curves

  1. #1
    Senior Member mollymcf2009's Avatar
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    Calc II - Area btw curves

    Hi, I have an area between curves problem that I am stuck on and I think it is because I need to use a double-angle identity in my figuring of my intersection points, but I don't know how to to this when I have coefficients that are greater than 2.
    Here is the problem:

    Find the area between the following curves:
    y=7cos(4x), y=7sin(8x) x=o x= pi/8

    I am trying to find where the first two intersect:
    7cos(4x) = 7sin(8x)

    7cos(4x) - 7sin(8x) = 0 *I factored out the 7. Should I reduce the 4x to x and the 8x to 2x and then use the double angle identity for sin2x?

    I keep getting my intersection as pi/2, which is not in the domain of the area limited by these curves.
    Any help is greatly appreciated! Thanks!
    Molly
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  2. #2
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    skeeter's Avatar
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    7\cos(4x) - 7\sin(8x) = 0

    7\cos(4x) - 14\sin(4x)\cos(4x) = 0

    7\cos(4x)[1 - 2\sin(4x)] = 0

    \cos(4x) = 0 ... x = \frac{\pi}{8}

    \sin(4x) = \frac{1}{2} ... x = \frac{\pi}{24}

    A = 7 \int_{\frac{\pi}{24}}^{\frac{\pi}{8}} \sin(8x) - \cos(4x) \, dx
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  3. #3
    Senior Member mollymcf2009's Avatar
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    Thank you so much!!
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