Tidal power plants use "tidal energy" to produce electrical energy. To construct a tidal power plant, a dam is built to separate a bay from the sea. The amount of natural energy produced depends on the volume of the bay and the tidal range -- the vertical distance between high and low tides.
The basin is formed by a 3-D rectangle with dimensions: 1000 ft wide, 500 ft in height and 25 ft in depth. The curve inside that 3-D rectangle that is given by the function:
y = (x^2/40000).
Consider a basin with a rectangular base. The basin has a tidal range of 25 feet, with low tide corresponding to y = 0. How much water does the basin hold at high tide?
I set up my integral as the following: (500)(25)(1000) * integral of (x^2/40000)dx from 0 to 25.
I have a feeling that I'm missing a step. Any help would be great, thanks!