20/08/09 23:46:18.36 wgUVJ5Xl.net
I_n = ∫[a,b] {(b-x)(x-a)}^n dx
= (b-a)^{2n+1} ∫[0,1] {t(1-t)}^n dt
= (b-a)^{2n+1} B(n+1,n+1)
= (b-a)^{2n+1} Γ(n+1)^2 /Γ(2n+2),
20/08/09 23:46:18.36 wgUVJ5Xl.net
I_n = ∫[a,b] {(b-x)(x-a)}^n dx
= (b-a)^{2n+1} ∫[0,1] {t(1-t)}^n dt
= (b-a)^{2n+1} B(n+1,n+1)
= (b-a)^{2n+1} Γ(n+1)^2 /Γ(2n+2),