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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One way to look at integration is of the inverse operation of differentiation. The derivative of x^2 is 2x; the integral of 2x gets you back to x^2.
The integral between two limits (values of the independent variable) gives you the area under the curve between those points. This can be useful for things such as calculating distance from a speed/time graph or for determining how much of a reactant is left in a chemical process after a certain length of time.
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