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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While it’s the opposite of derivative, undoing of derivative, it has another conceptual meaning: that is it’s the area under a curve and the x axis. Why is this important? Being able to calculate the area under curve gives a starting point for getting volume of weird shaped things such as a bottle. In higher calc classes(2, 3) the outward edge of the bottle can be modeled as a curve and that curve is rotated around an axes to get the volume. This where the power of calculus comes to play. A sphere, box, cylinder has volume formula, but what is the formula for any weirdly shaped stone? There is none. You have to use calculus.
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