Solve the triple integral $\iiint_D (x^2 + y^2 + z^2)\, dxdydz$ How does one go about solving the integral: 
$$
\iiint_D (x^2 + y^2 + z^2)\, dxdydz, 
$$
where 
$$
D=\{(x,y,z) \in \mathbb{R}^3: x^2 + y^2 + z^2 \le 9\}. 
$$
I believe I am supposed to convert to spherical coordinates but I would need some help with how this is done and what the answer to this integral would be.
Thanks in advance!

A quick way to evaluate it is to note that the volume of the spherical shell from radius $r$ to radius $r + \Delta r$ is approximately $4\pi r^2 \Delta r$, so your result should be
$$\int_0^3 r^2 (4\pi r^2) \,dr$$
$$= {4 \over 5} \pi r^5\bigg|_{r=0}^3$$
$$= {4 \over 5} 3^5 \pi$$
$$={972 \pi \over 5}$$
To do it properly you should do spherical coordinates like mathematics2x2life is trying to do.
