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Fundamental Theorem of Calculus

Why area-so-far recovers the integrand · BC Calculus · greeting

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Owl · Mock interview — Fundamental Theorem of Calculus. I ask; you answer.

Owl · Why should accumulation and antidifferentiation be two faces of the same idea — and what continuity assumptions quietly sit underneath?

Larry’s gold answer — Show text to read it out loud.

Larry · gold answer · If I nudge x by a tiny Δx, A gains roughly f(x)·Δx of area. Dividing by Δx and taking a limit suggests A′(x) ≈ f(x).

Owl: Why should accumulation and antidifferentiation be two faces of the same idea — and what continuity assumptions quietly sit underneath?

You: —