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It’s hardly related, but I once had a nightmare that I was back to high school and had to take an exam on integrals, but since I didn’t know anything I just repeated to the teacher (who strangely was my college teacher) that I was an arts student.
When I woke up, I asked my friends who were studying engineering what integrals were, none of them gave me a satisfactory answer, so to this day I still have no idea what they are.
Very simply:
- A function defines a curve.
- A derivative reveals the slope of that curve at a very specific point.
- An integral reveals the area “under” the curve (the space bounded by the curve and the horizontal axis).