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I need help with finding the volume of a 10-dimensional cube with a given interval: $1 \geq x \geq -1$. I tried to defined the function by: $a^2+b^2+c^2...j^2 \leq 1$ as the question required. I can not find the codes that works for this problem. Does anyone know how to solve it by using the Monte Carlo method or any other method?

David G. Stork
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Eda K
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1 Answers1

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You can use region functionality for this. 10-dimensional hypercube (trivial):

RegionMeasure @ Cuboid[-ConstantArray[1, 10], ConstantArray[1, 10]]

1024

10-dimensional hyperball:

RegionMeasure @ Ball[ConstantArray[0, 10]]

π^5/120

Carl Woll
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