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Date: 3-6-2019
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Date: 29-9-2018
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Date: 23-7-2019
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Inverse function integration is an indefinite integration technique. While simple, it is an interesting application of integration by parts.
If and
are inverses of each other on some closed interval, then
![]() |
(1) |
so
![]() |
(2) |
where
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(3) |
Therefore, if it is possible to find an inverse of
, integrate
, make the replacement
, and subtract the result from
to obtain the result for the original integral
.
If and
are elementary on some closed interval, then
is elementary iff
is elementary.
REFERENCES:
Key, E. "Disks, Shells, and Integrals of Inverse Functions." Coll. Math. J. 25, 136-138, 1994.
Parker, F. D. "Integrals of Inverse Functions." Amer. Math. Monthly 62, 439-440, 1955.
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