The image below is of the astroid curve [tex]x^{\frac{2}{3}}+y^{\frac{2}{3}}=2[/tex].
(a) Is it possible to use an integral in [tex]x[/tex] to compute the length of the curve in the first quadrant? What about an integral in [tex]y[/tex]? Why or why not?

(b) Use an integral in [tex]x[/tex] to compute the length of the curve between [tex](1, 1)[/tex] and [tex](0, 2^{\frac{3}{2}})[/tex].

(c) Use an integral in [tex]y[/tex] to compute the length of the curve between [tex](0, 2^{\frac{3}{2}})[/tex] and [tex](1, 1)[/tex].

Question

24-09-2022
Mathematics

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The image below is of the astroid curve [tex]x^{\frac{2}{3}}+y^{\frac{2}{3}}=2[/tex].
(a) Is it possible to use an integral in [tex]x[/tex] to compute the length of the curve in the first quadrant? What about an integral in [tex]y[/tex]? Why or why not?

(b) Use an integral in [tex]x[/tex] to compute the length of the curve between [tex](1, 1)[/tex] and [tex](0, 2^{\frac{3}{2}})[/tex].

(c) Use an integral in [tex]y[/tex] to compute the length of the curve between [tex](0, 2^{\frac{3}{2}})[/tex] and [tex](1, 1)[/tex].

$The image below is of the astroid curve texxfrac23yfrac232tex a Is it possible to use an integral in texxtex to compute the length of the curve in the first qua class=$

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