Computer Ave Value of f(x,y,z) over region W?

First of all, the volume ∫∫∫ 1 dW of the region W equals
∫(x = 0 to 1) ∫(y = 0 to x) ∫(z = 0 to y) 1 dz dy dx
= ∫(x = 0 to 1) ∫(y = 0 to x) y dy dx
= ∫(x = 0 to 1) (1/2)x^2 dx
= 1/6.

Hence, the average value of f over W equals
(1/(1/6)) ∫(x = 0 to 1) ∫(y = 0 to x) ∫(z = 0 to y) xyz dz dy dx
= ∫(x = 0 to 1) ∫(y = 0 to x) ∫(z = 0 to y) 6xyz dz dy dx
= ∫(x = 0 to 1) ∫(y = 0 to x) 3xyz^2 {for z = 0 to y} dy dx
= ∫(x = 0 to 1) ∫(y = 0 to x) 3xy^3 dy dx
= ∫(x = 0 to 1) (3/4)xy^4 {for y = 0 to x} dx
= ∫(x = 0 to 1) (3/4)x^5 dx
= (1/8) x^6 {for x = 0 to 1}
= 1/8.

I hope this helps!