Last updated on Sep 21, 2026

Definite Integration (AQA A-Level Mathematics): Quizzes

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Definite Integration

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What does definite integration yield, unlike indefinite integration?

A specific numerical value

If $f(x)$ has positive and negative values over $[a,b]$ , what does $\int_a^b f(x) \, dx$ give?

Net area

How do you find the total area regardless of whether $f(x)$ is above or below the x-axis?

Integrate the absolute value of $f(x)$

According to the Fundamental Theorem of Calculus, what is $\int_a^b f(x) \, dx$ equal to?

$F(b) - F(a)$

What happens to the constant $C$ when computing a definite integral?

It always cancels

What is the relationship between $\int_a^b f(x) \, dx$ and $\int_b^a f(x) \, dx$ ?

$\int_a^b f(x) \, dx = -\int_b^a f(x) \, dx$

What is the value of $\int_a^a f(x) \, dx$ ?

$0$

What does the additivity property state about $\int_a^b f(x) \, dx + \int_b^c f(x) \, dx$ ?

It equals $\int_a^c f(x) \, dx$

Which quantities in physics are calculated using definite integrals?

Displacement, work, and energy

What are the numbers $a$ and $b$ in the notation $\int_a^b f(x) \, dx$ called?

Limits

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