題目 Problem Find the average value of the function F(x,y,z)=x+y+zF(x,y,z) = x+y+zF(x,y,z)=x+y+z over the solid E:x2+y2+z2≤1,x≥0,y≥0,z≥0E: x^2+y^2+z^2 \le 1, x \ge 0, y \ge 0, z \ge 0E:x2+y2+z2≤1,x≥0,y≥0,z≥0. The formula for average value is 1Volume(E)∭EF(x,y,z)dV\displaystyle \frac{1}{\text{Volume}(E)} \iiint_E F(x,y,z) \mathrm{d}VVolume(E)1∭EF(x,y,z)dV.
