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Math Help - area

  1. #1
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    area

    find the area bounded by y^(2/3)+x^(2/3)=a^(2/3) and co-ordinate axes.
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  2. #2
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    Quote Originally Posted by ayushdadhwal View Post
    find the area bounded by y^(2/3)+x^(2/3)=a^(2/3) and co-ordinate axes.
    Do you mean the area in the first quadrant?

    y= (a^{2/3}- x^{2/3})^{3/2}

    I recommend the substitution x= u^3 to integrate that.
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by ayushdadhwal View Post
    find the area bounded by y^(2/3)+x^(2/3)=a^(2/3) and co-ordinate axes.
    Use the parametrization x=a\cos^3(t) and y=a\sin^3(t) to complete the simple close.

    By Greene's theorem we get

    \frac{1}{4}\iint_DdA=-\frac{1}{4}\oint y\,dx=-a^2\int_{0}^{2\pi}\sin^3(t)(3\cos(t)\sin(t))dt=-\frac{3a^2}{4}\int_{0}^{2\pi}\sin^{4}(t)\cos(t)\,d  t
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