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

f(x,y,z) = 18(x+y) W: y≤ z≤x ; 0≤y≤x ; 0≤x≤1

∭W (18(x+y))dV =

2 answers

well, forget the 18 for a while
18 ∭ (x+y)dz dy dx
integrate over z from y to x
18 integral (x+y)(x-y) dy dx
18 integral (x^2-y^2) dy from y = 0 to x dx
18 integral (x^3 -x^3/3) dx from x=0 to 1
18 [ (2/3) x ^3 dx ] from 0 to 1
12 (1^4/4)
3
check my arithmetic, did that fast !
Looks ok to me
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