It’s worth rehearsing that instinct. The insight that areas are products is a really useful one for deepening your intuition of what integration is doing, as well as for enhancing your ability to interpret graphs and charts.
Like, if you have a graph showing power consumption over time, it’s great to be able to mentally recognize that, say, if the time units are hours and the power units are Watts, that the area under the graph will be counted in Watt hours; that a rectangle one hour wide by one Watt tall is one Watt hour, and so on.
Like, if you have a graph showing power consumption over time, it’s great to be able to mentally recognize that, say, if the time units are hours and the power units are Watts, that the area under the graph will be counted in Watt hours; that a rectangle one hour wide by one Watt tall is one Watt hour, and so on.