As viewed from above, a swimming pool has the shape of the ellipse given by
The cross sections perpendicular to the ground and parallel to the -axis are squares. Find the total volume of the pool.
the plus part gives the curve above the x-axis, the minus part gives the curve below the x-axis.
recall, the volume is given by
where is the cross-sectional area.
note that here, is given by the formula for a square, where the side length is given by the difference between the two functions.