Last updated on Oct 23, 2026

Fundamental Theorem of Calculus (AQA A-Level Mathematics): Flashcards

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Fundamental Theorem of Calculus

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FTC links these two operations

Differentiation and integration

Number of parts in FTC

Two

FTC1: $F'(x)$ where $F(x) = \int_a^x f(t) dt$

$f(x)$

FTC1: Integrate then differentiate gives

Original function back

FTC2: $\int_a^b f(x) dx$ equals

$F(b) - F(a)$

FTC2 allows evaluation of definite integrals using

Antiderivatives

Differentiation & integration are (FTC)

Inverse processes

$F(x)$ if $F(x) = \int_0^x 2t dt$

$x^2$

Value of $\int_1^4 3x^2 dx$

$63$

FTC1 visual: $F(x)$ represents

Accumulated area under curve

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Integration

Further Integration

Differential Equations

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Integration

Further Integration

Differential Equations

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Integration

Further Integration

Differential Equations

Explore AQA A-Level Mathematics Exam Questions by Topics

Integration

Further Integration

Differential Equations

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