2 Attachment(s)

changing order of integration in spherical coordinates

Hi,

I'm teaching myself a bit of calculus and I'm having trouble with this:

Let *D* be the region bounded below by the plane z=0, above by the sphere x^2 + y^2 + z^2 = 4, and on the sides by the cylinder x^2 + y^2 = 1. Set up the triple integral in spherical coordinates that gives the volume of *D* using the order of integration .

The solution says that D is:

Attachment 18014

But I thought it should be:

Attachment 18015

Could you please tell me where I'm going wrong?

Many thanks!