eli5 why the area under a curve(or any line) is important
In: 0
“The area under the curve” rarely matters; specific cases in geometry. But that area represents result of an integral. Integral is a special function that takes a function (instead of just a variable) on input and produces another function on output. And integrals, alongside with derivatives (which do the same only in opposite direction) are very important and useful, changing “rate” into “value”
Take accelerometers, small chips, often found in phones, drones etc. They measure acceleration (including gravitational). In phones they’ll usually just change the screen orientation. But in drones – integral of acceleration is speed. Integral of speed is position. So passing the output of accelerometers through integration twice (and knowing the drone was lying immobile on the ground in the beginning) they can tell the drone where it is, and so tell it how to return to the starting point, or hold position, or follow a specific path.
In the opposite direction, your car’s speedometer runs a differential on the input of odometer; position/distance->speed.
Let’s add there’s a whole bunch of other integrals, not just “surface under the curve”. There’s length of the curve, there’s flow through a loop in a field (evocative: how much water in a river will flow into a pipe depending on its shape and orientation; practical: engineering stuff about magnetic fields – electromagnets, electric motors), volume integral (mass of a solid carved out of uneven density material), and a bunch of others so obscure I forgot them.
Latest Answers