I’m in CalcII now and for the life of me cannot wrap my head around integrals. Now we are using things like u-Substitution methods and solving the areas between 2 curves. I can understand how the equations work, but not why because I still cannot picture what an integral is or why it’s important.
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An integral creates a relationship between two semi-related dimensions. Say your x-axis is time and your y-axis is speed (or distance per unit time). When you take the integral of the data points presented (i.e. time * distance / time), you now have a new data point: distance.
If a device has an accelerometer, then you can track how far that device has moved without using other tech-expensive techniques like triangulation or GPS queries.
There’s countless gauges in smart-devices that rely on integrals to interpret data presented by gauges into something potentially more meaningful.
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