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Volume of a Hypersphere

Finding formulas for the volume enclosed by a hypersphere in n-dimensional space.

c) Use a quadruple integral to find the hypervolume enclosed by the hypersphere x^2 + y^2 + z^2 + w^2 = r^2 in R^4. (Use only trigonometric substitution and the reduction formulas for ∫sin^n(x)*dx or ∫cos^n(x)*dx.)

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Solution Summary

The volume of a hypersphere is found. The solution is detailed and well presented.