A glass vase has the shape of the solid obtained by rotating about the y-axis the area in the first quadrant lying over the x-interval [0,a] and under the graph of
Determine how much glass is contained in the vase.
As the curve is being rotated about the y-axis, we need the limits on the y-axis.
Also, we integrate the discs with radius=x.
The volume of the vase is
If the glass is the solid part under the graph above the x-axis, with a hollow interior above the graph,
subtract this integral from