Help with simple Triple Integral

Evaluate ∫∫∫ f(x,y,z)dV for the function f and region W specified:

∫∫∫f(x,y,z)=54(x+y) W: y
dV=

Work from the inner most integral first.

∫(x = 0 to 1) ∫(y = 0 to x) ∫(z = y to x) 54(x + y) dz dy dx
= ∫(x = 0 to 1) ∫(y = 0 to x) [∫(z = y to x) 54(x + y) dz] dy dx
= ∫(x = 0 to 1) ∫(y = 0 to x) 54(x + y) z {for z = y to x} dy dx
= ∫(x = 0 to 1) ∫(y = 0 to x) 54(x + y) (x - y) dy dx
= ∫(x = 0 to 1) [∫(y = 0 to x) (54x^2 - 54y^2) dy] dx
= ∫(x = 0 to 1) (54x^2 y - 18y^3) {for y = 0 to x} dx
= ∫(x = 0 to 1) 36x^3 dx
= 9x^4 {for x = 0 to 1}
= 9.

I hope this helps!