Fundamental theorem of calculus

About this app

Both parts of the fundamental theorem intuitively animated: d/dx ∫ₐˣ f = f(x) and ∫ₐᵇ f = F(b) − F(a). The shaded area under f and the height difference of the antiderivative F grow in lockstep — the core idea made tangible.

Subject: Analysis (one-dimensional)

More from Analysis (one-dimensional)

• Derivative as a sequence of secants
• Bounded growth
• Exponential growth and decay
• Optimisation: the largest rectangle
• Area between curves
• Area function is an antiderivative
• Sequential continuity
• Rational functions and asymptotes

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