Last updated on Oct 23, 2026

Area Under a Curve (AQA A-Level Mathematics): Quizzes

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Area Under a Curve

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What formula represents the area under curve $y = f(x)$ from $x = a$ to $x = b$ ?

$\int_a^b f(x) \, dx$

What does the definite integral compute when $f(x)$ changes sign over $[a, b]$ ?

Net area (positive minus negative)

If $f(x) \geq 0$ for all $x$ in $[a, b]$ , what does $\int_a^b f(x) \, dx$ give?

Total area under curve above x-axis

If $f(x) \leq 0$ for all $x$ in $[a, b]$ , what does the integral give?

Negative of the area

Using the Fundamental Theorem of Calculus, how is $\int_a^b f(x) \, dx$ evaluated?

$F(b) - F(a)$

What is the formula for area between curves $y = f(x)$ and $y = g(x)$ where $f(x) \geq g(x)$ ?

$\int_a^b [f(x) - g(x)] \, dx$

When a curve lies below the x-axis, how do you find the actual area?

Take absolute value of the integral

When part of curve is below x-axis, what should you do to find the area?

Integrate separately for each region

What is the antiderivative of $x^2$ ?

$\frac{x^3}{3}$

For area between two curves, which curve do you subtract from which?

Subtract lower from upper curve

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Area Under a Curve (AQA A-Level Mathematics): Quizzes

Practise the questions

What formula represents the area under curve y=f(x)y = f(x)y=f(x) from x=ax = ax=a to x=bx = bx=b?

What does the definite integral compute when f(x)f(x)f(x) changes sign over [a,b][a, b][a,b]?

If f(x)≥0f(x) \geq 0f(x)≥0 for all xxx in [a,b][a, b][a,b], what does ∫abf(x) dx\int_a^b f(x) \, dx∫ab​f(x)dx give?

If f(x)≤0f(x) \leq 0f(x)≤0 for all xxx in [a,b][a, b][a,b], what does the integral give?

Using the Fundamental Theorem of Calculus, how is ∫abf(x) dx\int_a^b f(x) \, dx∫ab​f(x)dx evaluated?

What is the formula for area between curves y=f(x)y = f(x)y=f(x) and y=g(x)y = g(x)y=g(x) where f(x)≥g(x)f(x) \geq g(x)f(x)≥g(x)?

When a curve lies below the x-axis, how do you find the actual area?

When part of curve is below x-axis, what should you do to find the area?

What is the antiderivative of x2x^2x2?

For area between two curves, which curve do you subtract from which?

Explore AQA A-Level Mathematics Revision Notes by Topics

Integration

Further Integration

Differential Equations

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Integration

Further Integration

Differential Equations

Explore AQA A-Level Mathematics Flashcards by Topics

Integration

Further Integration

Differential Equations

Explore AQA A-Level Mathematics Exam Questions by Topics

Integration

Further Integration

Differential Equations

Join 100,000+ A-Level students studying Quizzes with us.

What formula represents the area under curve $y = f(x)$ from $x = a$ to $x = b$ ?

What does the definite integral compute when $f(x)$ changes sign over $[a, b]$ ?

If $f(x) \geq 0$ for all $x$ in $[a, b]$ , what does $\int_a^b f(x) \, dx$ give?

If $f(x) \leq 0$ for all $x$ in $[a, b]$ , what does the integral give?

Using the Fundamental Theorem of Calculus, how is $\int_a^b f(x) \, dx$ evaluated?

What is the formula for area between curves $y = f(x)$ and $y = g(x)$ where $f(x) \geq g(x)$ ?

What is the antiderivative of $x^2$ ?