I am confused on how the bounds on the question are found. Here's the question.

Use spherical coordinates to find the mass of the solid enclosed by the hemispherical region $\displaystyle x^2+y^2+z^2<4$ and $\displaystyle 0<y$ with a density function (x,y,z)=

$\displaystyle \sqrt{1+(x^2+y^2+z^2)^\frac{3}{2})} $

also, the < signs are suppose to be "less than or equal to"