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Fundamental theorem of calculus and definite integrals

Understand the fundamental theorem of calculus, ∫ 𝑓(𝑥)𝑏 𝑎  𝑑𝑥= 𝐹(𝑏)− 𝐹(𝑎), and use it to calculate definite integrals.

mm-u4-t1-s1-d3

Interactive

Net area equals F(b) − F(a)

manipulative

Signed area under f from a to b matches the vertical gap F(b) − F(a) on any antiderivative — the fundamental theorem as two linked graphs.

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