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    Volume of a Hypersphere : n-Tuple Integral

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    Please do #4.

    Please see the attached file for full problem description.

    In this project, we find formulas for the enclosed by a hypersphere in n?dimensional spaces
    1 Use a double integral, and trigonometric substitution, together with Formula 64 in the Table of Integrals, to find the area of a circle with radius r

    2 Use a triple integral and trigonometric substitution to find the volume of a sphere with radius r.

    3 Use a quadruple integral to find the hypervolume enclosed by the hypersphere.....
    (Use only trigonometric substitution and the reduction formulas for....

    4 Use an n-tuple integral to find, the volume enclosed by a hypersphere of radius r in
    n-dimensionai space R [Hint: The formulas for n even and for n odd are different.]

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    Solution Summary

    The volume of a hypersphere is found in this well presented solution.