- 533 名前：１３２人目の素数さん [2012/02/08(水) 23:54:48.66 ]
- ∬_D (x+y)^2 * exp(x-y) dxdy
D={(x,y):|x|+|y| <= 1}
x+y=u,x-y=v
dudv=|(u,v/x,y)|=|(1,1;1,-1)|=2dxdy
(u,v)=(-1,1)x(-1,1)
1/2u^2e^vdudv=1/2u^3/3e^v=.5(1/3+1/3)(e-1/e)=(1/3)(e-1/e)
du=dx+dy
dv=dx-dy
du^dv=-dx^dy-dx^dy=-2dx^dy
dx^dy=-.5du^dv
