Apa itu Teorema Dasar Kalkulus?

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Area under x² from 0 to 2: antiderivative gives exact answer

∫₀² x² dx = [x³/3]₀² = 8/3 − 0 = 8/3 ≈ 2.667. The antiderivative F(x) = x³/3 gives the exact area without approximation.

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The two parts of the Fundamental Theorem of Calculus

Part 1: d/dx [∫ₐˣ f(t)dt] = f(x)

Part 2: ∫ₐᵇ f(x)dx = F(b) − F(a) where F'(x) = f(x)

Part 1 says differentiation undoes integrasion. Part 2 says to evaluate an integral, find an antiderivative dan subtract the endpoints.

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Riemann sum approximating area: FTC replaces this with one calculation

A Riemann sum with 8 rectangles gives ≈ 0.273. The exact answer is 8/3 ≈ 2.667. The Fundamental Theorem gives exact results with no rectangles needed.

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