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Quantum Chemistry/Integration by parts
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Example Problem:
Evaluate the triple integral shown below in spherical polar coordinates using the given boundary conditions:
Solution:
The triple integral can be rewritten as an iterated integral under the boundary conditions as follows:
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The integral can then be evaluated using Fubini's theorem to separate the multivariable integrals into single variable integrals that can be solved accordingly as follows:
=
Multiplying these results together then gives the final solution:
(2) =
Therefore,
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