Why finding areas under curves is actually an exercise in subtraction
In short: The second part of the Fundamental Theorem of Calculus can feel like a magic trick, but it relies on a logical bridge between accumulation and change. This video explains why we use antiderivatives to solve definite integrals.
The theorem establishes that the definite integral of a function from one point to another is equal to the difference between the values of its antiderivative at those two points. Instead of summing infinite tiny slices, we can simply find a function whose derivative matches our original curve and calculate the change in its value.
By understanding this intuition, students can see that integration isn't just an isolated rule for area; it is deeply connected to the reverse process of differentiation.
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Sources
- Summary by Intellect · source: Intuition for second part of fundamental theorem of calculus | AP Calculus AB | Khan Academy
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