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Integral oddity - lrdheat - 07-31-2016 09:06 PM
Integral 1/(x^2 * sqrt(x^2 + 4)) should be (-sqrt(x^2 + 4))/4*x
The prime gives (-x -sqrt(x^2 + 4))/4*x after factorizing or after simplifying. Is this a bug?
RE: Integral oddity - lrdheat - 07-31-2016 09:07 PM
Version 2016 04 14 (10077)
RE: Integral oddity - lrdheat - 07-31-2016 09:14 PM
When integrating over a specific range such as pi/6 to pi/4, the exact answer converts to a correct approximate answer of ~.303
Am I missing something?
RE: Integral oddity - parisse - 08-01-2016 06:17 AM
(07-31-2016 09:06 PM)lrdheat Wrote: Integral 1/(x^2 * sqrt(x^2 + 4)) should be (-sqrt(x^2 + 4))/4*x
The prime gives (-x -sqrt(x^2 + 4))/4*x after factorizing or after simplifying. Is this a bug?
No, because antiderivatives are defined up to a constant.
RE: Integral oddity - lrdheat - 08-01-2016 10:08 PM
I must be math challenged/rusty...is not the "-x" that Prime produced a variable? How are the 2 answers equivalent?
What has me befuddled is that when made into a definite integral, Prime reports a correct answer.
RE: Integral oddity - Dieter - 08-01-2016 11:14 PM
(08-01-2016 10:08 PM)lrdheat Wrote: I must be math challenged/rusty...is not the "-x" that Prime produced a variable? How are the 2 answers equivalent?
If you simplify the Prime result...
Code:
–x – sqrt(x²+4)
---------------
4x
–x sqrt(x²+4)
= -- – ----------
4x 4x
sqrt(x²+4)
= –1/4 – ----------
4x
sqrt(x²+4)
= const – ----------
4x...you get the same antiderivative plus a constant.
Dieter
RE: Integral oddity - lrdheat - 08-02-2016 02:10 AM
Thanks!
For some reason, I was seeing the denominator as "4" instead of "4*x".