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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The premise of an integral is to get information using what you know, generally the rate of change. If we know a car is accelerating 10 miles per hour, we don’t know how fast it’s going but we can figure out how much faster it has gone, and in addition, how much more MORE distance it’s covered as a result of that acceleration. If we gain the knowledge of how fast that car WAS going, we now know not only how fast it is now but can also determine the distance it traveled.
I might suck at where the words come from here, but when you take the derivative, you’re finding what measurement caused the other measurement, or what derived it, like speed causing a change in position or speed being derived from acceleration. When you integrate, you’re integrating (bringing all of these things together) to figure out what the speed or position was.
I have a hunch I’m WAAAY above the ELI5 here, but outside of word problems most of the math in this area is going to be abstract and not very intuitive.
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