Fundamental Theorem of Calculus (AQA 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

If F(x)=∫axf(t) dtF(x) = \int_a^x f(t) \, dt, what is F′(x)F'(x)?

f(x)f(x)

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

We get back the original function

If F(x)F(x) is an antiderivative of f(x)f(x), what does ∫abf(x) dx\int_a^b f(x) \, dx equal?

F(b)−F(a)F(b) - F(a)

What does FTC2 allow us to use for evaluating definite integrals?

Antiderivatives directly

If f(x)=2xf(x) = 2x, what is F(x)=∫0x2t dtF(x) = \int_0^x 2t \, dt?

x2x^2

What is the value of ∫143x2 dx\int_1^4 3x^2 \, dx?

63

In FTC1, what does F(x)F(x) represent visually?

Accumulated area under the curve

How are differentiation and integration related according to the FTC?

Essentially inverse processes

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