Re: Bug in Mathematica ?
- To: mathgroup at smc.vnet.net
- Subject: [mg60840] Re: Bug in Mathematica ?
- From: Peter Pein <petsie at dordos.net>
- Date: Fri, 30 Sep 2005 03:57:08 -0400 (EDT)
- References: <dhdbeu$8fk$1@smc.vnet.net> <dhgf81$20o$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Klaus G. schrieb: > Strangely enough, Integrate[Min[x, y], {x, 0, a}, {y, 0, b}] results in > a^3/6. > Must be a bug?! > > Klaus G. > Hi Klaus, not really a bug: In[1]:= Assuming[{a, b} \[Element] Reals, Integrate[Min[x, y], {x, 0, a}, {y, 0, b}]]// InputForm Out[1]//InputForm= Piecewise[ {{a^3/3, a - b == 0 && a < 0 && b == 0}, {(a^2*b)/2, a < 0 && b > 0 && a - b < 0}, {(a*b^2)/2, a > 0 && a - b > 0 && b < 0}, {b^3/6, a - b == 0 && b == 0 && a > 0}, {b^3/3, a > 0 && b > 0 && a - b >= 0}, {(-a^3 + 3*a^2*b)/6, a > 0 && b >= 0 && a - b < 0}, {(2*a^3 + 3*a^2*b)/6, a < 0 && b > 0 && a - b == 0}, {(a^3 + 3*a*b^2)/6, a - b > 0 && a < 0 && b <= 0}, {(-a^3 + 3*a^2*b + 3*a*b^2)/6, a > 0 && a - b < 0 && b < 0}, {(a^3 + 3*a^2*b + 3*a*b^2)/6, a < 0 && b > 0 && a - b > 0}, {(3*a*b^2 - 2*b^3)/6, a > 0 && a - b > 0 && b > 0}, {(a^3 + b^3)/3, a - b == 0 && a < 0 && b < 0}, {(3*a^2*b + b^3)/6, a - b < 0 && b < 0 && a < 0}, {(3*a*b^2 + b^3)/6, a - b == 0 && a > 0 && b < 0}}, 0 ] In[2]:= FullSimplify[%,{a,b}\[Element]Reals]//InputForm Out[2]//InputForm= Piecewise[ {{(a^2*b)/2, b > 0 && a < 0 && a < b}, {(a*b^2)/2, a > 0 && a > b && b < 0}, {b^3/3, a > 0 && b > 0 && a >= b}, {-(a^2*(a - 3*b))/6, a > 0 && b >= 0 && a < b}, {(a^3 + 3*a*b^2)/6, a > b && a < 0 && b <= 0}, {(a^3 + b^3)/3, a == b && a < 0 && b < 0}, {(3*a^2*b + b^3)/6, a < 0 && a < b && b < 0}}, 0 ]