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 takes a rate of change, and turns it into a graph (the opposite of a derivative). It also gives you the area under a given graph (because a graph is the rate of change of the area beneath it, no?).
This is incredibly useful when you’re dealing with something complex that’s changing in a particular way. In practical terms, an integral is just breaking down a complex problem into incredibly small pieces, solving those pieces individually, and bringing them back together; integrating the answers.
This video does a nice job at showing how to think of integrals: [https://youtu.be/WUvTyaaNkzM](https://youtu.be/WUvTyaaNkzM)
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