Inverse Function Integration
المؤلف:
Key, E.
المصدر:
"Disks, Shells, and Integrals of Inverse Functions." Coll. Math. J. 25
الجزء والصفحة:
...
17-9-2018
1914
Inverse Function Integration
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
 |
(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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