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Math Help - Area between two polar curves

  1. #1
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    Area between two polar curves

    I am having difficulty finding the area between these two curves:

    <br />
r = \sin{2\Theta} and r = \cos{2\Theta}

    I setup the integral like this:

    <br />
\int_{0}^{\pi^/8}1/2(\cos{2\Theta}^2 - \sin{2\Theta}^2) d\Theta<br />

    I multiply the answer of the integral by 16 for the 16 parts of the graph but I cannot arrive at the right answer.
    Any help is appreciated of where I am going wrong.

    Thanks
    Last edited by mr fantastic; September 2nd 2010 at 05:08 PM. Reason: Format.
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  2. #2
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    Quote Originally Posted by evant8950 View Post
    I am having difficulty finding the area between these two curves:

    <br />
r = \sin{2\Theta} and r = \cos{2\Theta}

    I setup the integral like this:

    <br />
\int_{0}^{\pi^/8}1/2(\cos{2\Theta}^2 - \sin{2\Theta}^2) d\Theta<br />

    I multiply the answer of the integral by 16 for the 16 parts of the graph but I cannot arrive at the right answer.
    Any help is appreciated of where I am going wrong.

    Thanks
    Draw the graphs of each. Although they intersect at the origin, the point with polar coordinates [0, 0] is NOT common to both curves ....
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Draw the graphs of each. Although they intersect at the origin, the point with polar coordinates [0, 0] is NOT common to both curves ....
    When I set them equal I get they intersect at \pi/8. How do I find the other point of intersection?

    Thanks
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