Integrate Result depends on symbol used
- To: mathgroup at smc.vnet.net
- Subject: [mg42815] Integrate Result depends on symbol used
- From: hanson at physics.auburn.edu (Jim Hanson)
- Date: Wed, 30 Jul 2003 04:07:47 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Mathematica's ability to do a definite integral depends on the symbol
used.
Here's an example with Mathematica 5.0.0.0 on a Macintosh running OSX 10.2.6.
Note that Mathematica can do the integral with a symbol z
(which comes after the variable of integration y in the alphabet) but
can't do it with a symbol x. This seems very odd to me. Does anyone
know why this happens?
In[1]:= Integrate[Sqrt[y - x]/(y^2 Sqrt[1 - y^2]), { y , x, 1},
Assumptions -> {x > 0, x < 1}]
Sqrt[-x + y]
Out[1]= Integrate[---------------, {y, x, 1}, Assumptions -> {x > 0, x
< 1}]
2 2
y Sqrt[1 - y ]
In[2]:= Integrate[Sqrt[y - z]/(y^2 Sqrt[1 - y^2]), {y, z, 1},
Assumptions -> {z > 0, z < 1}]
2
Out[2]= (Pi (------- -
Sqrt[z]
1 1 3 1 5 2
2 Sqrt[2 Pi] HypergeometricPFQ[{-(-), -, -}, {-, -}, z ]
4 4 4 2 4
> -------------------------------------------------------- +
1 5
Gamma[-] Gamma[-]
4 4
1 3 5 3 7 2
Sqrt[2 Pi] z HypergeometricPFQ[{-, -, -}, {-, -}, z ]
4 4 4 2 4
> -----------------------------------------------------)) / 4
1 7
Gamma[-(-)] Gamma[-]
4 4