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Hypervolume Find the volume of the four-dimensional
Chapter 13, Problem 67(choose chapter or problem)
QUESTION:
Hypervolume Find the volume of the four-dimensional pyramid bounded by w + x + y + z + 1 = 0 and the coordinate planes w = 0, x = 0, y = 0, and z = 0.
Questions & Answers
QUESTION:
Hypervolume Find the volume of the four-dimensional pyramid bounded by w + x + y + z + 1 = 0 and the coordinate planes w = 0, x = 0, y = 0, and z = 0.
ANSWER:Step 1 of 3
We have to find out the hyper-volume of the four-dimensional pyramid bounded by
and the coordinate planes
Because play similar roles in the equation, the order of integration is probably
immaterial, and we can arbitrarily choose .
From the order , we first determine the bounds for .
.
Similarly, we can find the boundaries for .