I＝
∬
Dxy
f‘’xy(x，y)dxdy＝
∫10xdx
∫10y
f‘’xy(x，y)dy
∵
∫10y
f‘’xy(x，y)dy＝
∫10yd
f’x(x，y)＝y
f’x(x，y)
|10−
∫10
f’x(xy)dy
∴I＝
∫10xdx
∫10y
f‘’xy(x，y)dy＝
∫10x
f’x(x，1)dx−
∫10xdx
∫10
f’x(x，y)dy
=Xf(x，1)
|10−
∫10xdx
∫10y
f’x(x，y)dy＝−
∫10dy
∫10xfx’(x，y)dx
=−[
∫10xf(x，y)
|10dy−
∫10dy
∫10f(x，y)dx]
=
∫10dy
∫