Much of the earth's photosynthesis occurs in the oceans. The rate of primary production depends on light intensity, measured as the flux of photons (that is, number of photons per unit area per unit time). For monochromatic light, intensity attenuates with water depth according to Beer's Law, which states that I(x) = e−kx, where x is water depth. A simple model for the relationship between rate of photosynthesis and light intensity is P(I) = aI, where a is a constant and P is measured as a mass of carbon fixed per volume of water, per unit time.† Calculate [infinity] P(I(x)) dx 0 .