From the course: Assembling Calculus
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Adding up changes: Integrals
From the course: Assembling Calculus
Adding up changes: Integrals
- [Instructor] In the previous movie, we took a curve and created a derivative curve from it. What happens if we try to go backwards and go from the derivative curve back to the original? Well, if our original curve starts at zero and we're tracking the changes from one point to another, we should just be able to go back to accumulate the changes to get the original curve back. Let's try it. The original curve starts out at zero, so we're consistent there. Then the next difference is one, and we match the original curve there. Next, we add one to three and get our next point on the original curve of four. And adding that four to the five in the derivative curve gives us nine. And finally, we add seven to nine to get 16. And indeed, the cumulative sum of the differences gives us back the original curve. This process of adding up the cumulative area of any curve is called integrating it or taking its integral. So we go…
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