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Harlamova29_29
[7]
3 years ago
7
(6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Use an iterated integral to compute the vo
lume of the ellipsoid x^2/a^2 + y^2/b^2 + z^2/c^2 = 1. The a, b, and c are positive constants.
Mathematics
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1
answer:
kipiarov
[429]
3 years ago
8
0
Let
be the ellipsoid with equation
so that the volume of
is given by the triple integral
Consider the augmented spherical coordinates given by the identities
Computing the Jacobian, we find that the volume element is given by
so that the volume integral can be written as
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