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  • 2 years ago

Calculus 3 Problem: Use an nᵗʰ-tuple integral to find the volume enclosed by a hypersphere of radius r in n−dimensional space. Hint: The formulas will be different for n even and n odd.

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  1. zepdrix
    • 2 years ago
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    Leading up to this, I had to do this for a circle, then a sphere, and then 4 dimensions. Trying to recognize the pattern...\[\large x_1^2+x_2^2+...+x_n^2=r^2\] \[\large x_1=\sqrt{r^2-x_n^2-x_{n-1}^2-...-x_2^2}\]

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