Last updated on Oct 23, 2026

Fundamental Theorem of Calculus (Edexcel A-Level Mathematics): Quizzes

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Fundamental Theorem of Calculus

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What two fundamental operations does the FTC link?

Differentiation and integration

How many parts does the Fundamental Theorem of Calculus have?

Two

In FTC1, if $F(x) = \int_a^x f(t) \, dt$ , what is $F'(x)$ equal to?

$f(x)$

What does FTC1 tell us about integrating then differentiating a function?

We get back the original function

According to FTC2, how do we evaluate $\int_a^b f(x) \, dx$ using antiderivative $F(x)$ ?

$F(b) - F(a)$

What does FTC2 allow us to avoid when evaluating definite integrals?

The limiting process of Riemann sums

If $f(x) = 2x$ and $F(x) = \int_0^x 2t \, dt$ , what is $F(x)$ equal to?

$x^2$

What is the value of $\int_1^4 3x^2 \, dx$ ?

$63$

How are differentiation and integration related according to the FTC?

They are essentially inverse processes

In FTC1 visualisation, what does $F'(x)$ represent?

The height of the curve at $x$

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Integration

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Further Integration

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Further Integration

Differential Equations

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