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Math Help - Area and Arc Length of |y|^n+|x|^n=a^n

  1. #1
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    Area and Arc Length of |y|^n+|x|^n=a^n

    I've been trying to fing both the area and the arc length of
    |y|^n+|x|^n=a^n
    with respect to x where a and n are constants

    Graphing examples of the function as well as solving simple examples where a=1 and n=1 (diamond) or n=2 (circle) has shown that the graph is symetrical in all quadrants.

    I've written the in equation terms of y and set limits to account for the symetry and have gotten.
    A(x)=4 \int_0^a (a^n-x^n)^{(1/n)}
    for the area and
    L(x)=4 \int_0^a \sqrt{1+(d/dx(a^n-x^n)^{(1/n)})}
    But I do not how to procede from there.
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  2. #2
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    I think the power of the integral becomes (n+1)/n but i don't know how to handle the (a^n-x^n) portion
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  3. #3
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    Anyone? I still can't figure it out.
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