When using shells, the cross sections are parallel to the axis we are revolving about. In this case, we are revolving about y so the cross sections will be parallel to the y-axis and 'stacked up' along the x-axis.

So, integrate in terms of x.

What we have here is a hemisphere of radius 2.

Solving the given equation for y in terms of x gives:

Since we are bounded by the axes, we are in the positive region:

Check your result using the volume of a hemisphere formula.