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Math Help - Polar curves area question

  1. #1
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    Polar curves area question

    I'm stuck on this question. I'm not sure what the lower and upper limits area.

    Find the area of the region that lies inside both curves.

    r = 1+cos(theta), r = 1-cos(theta)

    Thanks.
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  2. #2
    Member Abu-Khalil's Avatar
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    I suggest you to do a graph. The area is given by 4\frac{1}{2}\int_0^\frac{\pi}{2}(1-\cos\theta)^2d\theta.
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  3. #3
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    Thanks for your help. I did draw out a graph but was still confused. How did you find the limits of integration?
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  4. #4
    Member Abu-Khalil's Avatar
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    Drawing out a graph or notice that \cos x = \cos (2\pi - x)=-\cos (\pi+x). So 1-\cos \theta it's symmetrical with x-axis and 1+\cos \theta is 1-\cos \theta reflection with y-axis.
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