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Math Help - Area of a rose petal using Green's Theorem

  1. #1
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    Area of a rose petal using Green's Theorem

    Use Green's theorem to compute the area of one petal of the 16-leafed rose defined by r = 13sin(8t).

    It may be useful for recall that the area of a region D enclosed by a curve C can be expressed as A = (1/2)*integral(xdy - ydx).

    Attempt at a solution:

    I've got that the limit of theta should be from 0 to pi/8.

    x = 13sin(8t)*cos(t)
    y = 13sin(8t)*sin(t)

    dx = [104cos(8t)*cos(t) - 13sin(8t)*sin(t)]dt
    dy = [104cos(8t)*sin(t) + 13sin(8t)*cos(t)]dt

    A = (1/2)*integral(13sin(8t)*cos(t)*[104cos(8t)*sin(t) + 13sin(8t)*cos(t)]dt - 13sin(8t)*sin(t)*[104cos(8t)*cos(t) - 13sin(8t)*sin(t)]dt)

    I'm not sure how go about evaluating this integral.
    Last edited by My Little Pony; February 23rd 2010 at 09:06 AM.
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  2. #2
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    Okay, I've simplified the integral to:

    A = (1/2)*integral(13sin^2(8t))

    I evaluate it and get 13pi/32, as t goes from 0 to pi/8, but it says that is not correct. Anyone know if I'm simplifying the integral properly?
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