设物体放置在空间坐标系中的边界曲面为x=0，y=0，z=0和x+y+z=1的空间，又该物体每一点的密度μ(x，yx)=x，求该
物体的质量m．
令Ω={(x,y，z)∣0≤x≤1，0≤y≤1-x,0≤z≤1-x-y}则质量m为 m=∫∫∫Ωμ(x，y,z)dυ=∫∫∫Ωzdυ =∫01dx∫01-xdy∫01-x-yzdz=(1/2) ∫01dx∫01-x(1-x-y)2dy． =-(1/2)∫01dx∫01-x (1-x-y)2 d(1-x-y) =-(1/2)∫011/3(1-x-y)3∣01-xdx =1/6∫01(1-x)3dx=-(1/6)∫01(1-x)3d(1-x) =-(1/6)•(1/4)(1-x)4∣01=1/24
