Question

Let
S = {(x, y, z) ∈ $\R^3$ : x2 + y2 + z2 < 1}.
Then, the value of
$\frac{1}{\pi}\iiint_s\left((x-2y+z)^2+(2x-y-z)+(x-y+2z)^2\right)dxdydz$
equals ________ (rounded off to two decimal places).

Answer 1

The correct answer is 4.70 to 4.90. (approx)