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Math Help - are bound by polar coordinates

  1. #1
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    are bound by polar coordinates

    could someone please explain this:
    find the area bound by the curve r= a(1-sin theta) between theat = 0 and theta = 2pi.
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  2. #2
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    Quote Originally Posted by hyzlemon View Post
    could someone please explain this:
    find the area bound by the curve r= a(1-sin theta) between theat = 0 and theta = 2pi.
    Assuming that a is a constant and the integral is taken with respect to \theta...

    \int_0^{2\pi}{a(1 - \sin{\theta})\,d\theta} = a\int_0^{2\pi}{1 - \sin{\theta}\,d\theta}

     = a\left[\theta + \cos{\theta}\right]_0^{2\pi}

     = a\left[\left(2\pi + \cos{2\pi}\right) - \left(0 + \cos{0}\right)\right]

     = a\left(2\pi + 1 - 0 - 1\right)

     = 2\pi a.
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