Question: A river follows the path y = f(x) where x, y are in kilometers. Near the sea, it widens into a lagoon, then narrows again at its mouth. See Figure. At the point (x, y), the depth, d(x, y), of the lagoon is given by
d(x, y) = 40 - 160(y - f(x))2 - 40x2 meters.
The lagoon itself is described by d(x, y) ≥ 0. What is the volume of the lagoon in cubic meters?
